Consider the hypothesis statement to the right using alphaequals0.01 and the data to the right from two independent samples. ​a) Calculate the appropriate test statistic and interpret the result. ​b) Calculate the​ p-value and interpret the result. Click here to view page 1 of the standard normal table. LOADING... Click here to view page 2 of the standard normal table. LOADING... H0​: mu1minusmu2less than or equals0 H1​: mu1minusmu2greater than0 x overbar1 equals 88 x overbar2 equals 82 sigma1 equals 24 sigma2 equals 20 n1 equals 45 n2 equals 55 ​a) The test statistic is nothing. ​(Round to two decimal places as​ needed.)

Consider the following table:

Copy Data

Calculate the Sum of Squared Regression. Round your answer to two decimal places, if necessary.

Calculate the Degrees of Freedom among Regression.

Calculate the Mean Squared Regression. Round your answer to two decimal places, if necessary.

Calculate the value of the test statistic. Round your answer to two decimal places, if necessary.

How much of the variation in the dependent variable is explained by the regression? Round your answer to two decimal places, if necessary.

What proportion of the variation is explained by the regression? Round your answer to two decimal places, if necessary.

What is the estimated variance of the error terms? Round your answer to two decimal places, if necessary.

What is the total variability of the dependent variable? Round your answer to two decimal places, if necessary.

What is the variance of the dependent variable? Round your answer to two decimal places, if necessary.

Billy-Sean O'Hagan has joined the Physics Society at Suburban State University, and the group is planning to raise money to support the dying space program by making and selling umbrellas. The society intends to make three models: the Sprinkle, the Storm, and the Hurricane. The amounts of cloth, metal, and wood used in making each model are given in this table.

The table also shows the amounts of each material available in a given day and the profits to be made from each model. How many of each model should the society make to maximize its profit?

Sprinkle_______ umbrellas

Storm________ umbrellas

Hurricane_______ umbrellas

The accompanying data on degree of spirituality for a sample of natural scientists and a sample of social scientists working at research universities appeared in a paper. Assume that it is reasonable to regard these two samples as representative of natural and social scientists at research universities. Is there evidence that the spirituality category proportions are not the same for natural and social scientists? Test the relevant hypotheses using a significance level of 0.01.

State the null and alternative hypotheses.

H₀: The spirituality category for natural scientists and social scientists are not independent.
H_a: The spirituality category for natural scientists and social scientists are independent.

H₀: The spirituality category proportions are the same for natural scientists and social scientists.
H_a: The spirituality category proportions are not all the same for natural scientists and social scientists.    

H₀: The spirituality category for natural scientists and social scientists are independent.
H_a: The spirituality category for natural scientists and social scientists are not independent.

H₀: The spirituality category proportions are not all the same for natural scientists and social scientists.
H_a: The spirituality category proportions are the same for natural scientists and social scientists.

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =  

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =  

What can you conclude?

Do not reject H₀. There is not enough evidence to conclude that the spirituality category proportions are not all the same for natural scientists and social scientists.

Do not reject H₀. There is not enough evidence to conclude that there is an association between natural scientists and social scientists.    

Reject H₀. There is convincing evidence to conclude that there is an association between natural scientists and social scientists.

Reject H₀. There is convincing evidence to conclude that the spirituality category proportions are not all the same for natural scientists and social scientists.

A social psychologist is interested in how optimism is related to life satisfaction. A sample of individuals categorized as optimistic were asked about past, present, and projected future satisfaction with their lives. Higher scores on the life satisfaction measure indicate more satisfaction. Below are the data. What can the psychologist conclude with α = 0.05?

Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  

Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =   
2 vs. 3: difference =   

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =   
2 vs. 3: test statistic =  

The authors of a paper concerned about racial stereotypes in television counted the number of times that characters of different ethnicities appeared in commercials aired on a certain city's television stations, resulting in the data in the accompanying table.

Based on the 2000 Census, the proportion of the U.S. population falling into each of these four ethnic groups are 0.177 for African-American, 0.032 for Asian, 0.734 for Caucasian, and 0.057 for Hispanic. Do the data provide sufficient evidence to conclude that the proportions appearing in commercials are not the same as the census proportions? Test the relevant hypotheses using a significance level of 0.01.

Let p₁, p₂, p₃, and p₄ be the proportions of appearances of the four ethnicities across all commercials.

State the null and alternative hypotheses.

H₀: p₁ = p₂ = p₃ = p₄ = 0.177
H_a: H₀ is not true.

H₀: p₁ = p₂ = p₃ = p₄ = 69.738
H_a: H₀ is not true.    

H₀: p₁ = 0.177, p₂ = 0.032, p₃ = 0.734, p₄ = 0.057
H_a: H₀ is not true.

H₀: p₁ = p₂ = p₃ = p₄ = 56
H_a: H₀ is not true.

H₀: p₁ = 69.738, p₂ = 12.608, p₃ = 289.196, p₄ = 22.458
H_a: H₀ is not true.

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =  

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =  

What can you conclude?

Do not reject H₀. There is convincing evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.

Reject H₀. There is not enough evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.     

Reject H₀. There is convincing evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.

Do not reject H₀. There is not enough evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.

Assume the sample is taken from a normally distributed population. Construct

9595​%

confidence intervals for​ (a) the population variance

sigmaσsquared2

and​ (b) the population standard deviation

sigmaσ.

​(a) The confidence interval for the population variance is

​(nothing​,nothing​).

​(Round to three decimal places as​ needed.)

An article compared the drug use of 288 randomly selected high school seniors exposed to a drug education program (DARE) and 335 randomly selected high school seniors who were not exposed to such a program. Data for marijuana use are given in the accompanying table.

Is there evidence that the proportion using marijuana is lower for students exposed to the DARE program? Use α = 0.05.(Use p_DARE − p_{No DARE}. Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

P-value=

State your conclusion.

We reject H₀. We do not have convincing evidence that the proportion of students using marijuana is lower for students exposed to the DARE program than for students not exposed to the program.

We fail to reject H₀. We have convincing evidence that the proportion of students using marijuana is lower for students exposed to the DARE program than for students not exposed to the program.    

We reject H₀. We have convincing evidence that the proportion of students using marijuana is lower for students exposed to the DARE program than for students not exposed to the program.

We fail to reject H₀. We do not have convincing evidence that the proportion of students using marijuana is lower for students exposed to the DARE program than for students not exposed to the program.

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of women receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 are in following table:

Data of Health Expenditure versus Prenatal Care

Test at the 5% level for a correlation between percentage spent on health expenditure and the percentage of women receiving prenatal care. Then compute a 95% prediction interval for the percentage of woman receiving prenatal care for a country that spends 5.0 % of GDP on health expenditure.

(i) Which of the following statements correctly define both the null hypothesis H_Oand the alternate hypothesis H_A ?

A.   H_O :  ρ = 0   H_A :  ρ < 0

B.     H_O :  ρ > 0   H_A :  ρ = 0

C.   H_O :  ρ = 0   H_A :  ρ > 0

D.     none of these answers are correct

(ii) Enter the level of significance α used for this test, and the degrees of freedomdf:

Enter level of significance in decimal form to nearest hundredth, followed by comma, followed by degrees of freedom value to nearest integer. Do not enter spaces.  

Examples of correctly entered answers:  0.01,4    0.02,11    0.05,13    0.10,46

(iii)   Use technology to determine correlation coefficient r between independent variable (percent GDP spent on healthcare) and dependent variable (percent women receiving prenatal care)

Enter in decimal form to nearest ten-thousandth with sign. Examples of correctly entered answers:  

-0.0001    +0.0020    -0.0500    +0.3000    +0.7115

(iv)  Calculate and enter test statistic

Enter value in decimal form rounded to nearest hundredth, with appropriate sign (no spaces). Examples of correctly entered answers:

–2.10      –0.07        +0.60        +1.09

(v) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers:

0.000     0.001     0.030     0.600      0.814 1.000

(vi) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?  

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

Enter letter corresponding to correct answer.

(vii) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Evidence supports the claim that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to show that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

C. The result is not statistically significant at .05 level of significance. Evidence supports the claim that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

D. The result is not statistically significant at .05 level of significance.   There is not enough evidence to show that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

Enter letter corresponding to most correct answer

(viii) Determine standard error of the estimate s_e:

Enter answer to nearest hundredth

(ix) Compute a 95% prediction interval for the percentage of woman receiving prenatal care for a country that spends 5.0 % of GDP on health expenditure. Do this by:

• finding t_c(two-tailed t-score using level of significance and df value found in part (ii))  https://www.danielsoper.com/statcalc/calculator.aspx?id=10

• find "y^" output value corresponding to x_o = 5.0 using line-of-best-fit regression equation y^ =mx_o + b

• determining bound E using the following formula: (s_e , n , sample mean for x , and sample variance for x all can be found using http://vassarstats.net/index.html )

E=(tc) (se) (1+1n+( xo−x )2(sx2)(n−1)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ )E=tc se 1+1n+ xo-x 2sx2n-1

• subtract, then add bound E to y^ value to create prediction interval.

Determine which of the following 95% prediction intervals is most correct:

A. 39.42% < y < 116.41%

B. 23.29% < y < 132.55%

C. 47.65% < y < 108.19%

D. 40.89% < y < 114.94%

Enter letter corresponding to most correct answer

(x) Which of the following statements correctly interprets the significance of the prediction interval?

A. We estimate with 95% confidence that the interval 39.42% < y < 116.41% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

B. We estimate with 95% confidence that the interval 47.65% < y < 108.19% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

C. We estimate with 95% confidence that the interval 40.89% < y < 114.94% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

D. We estimate with 95% confidence that the interval 23.29% < y < 132.55% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

In a study of memory process, rats were first presented with a fear-inducing stimulus on a learning task as soon as they stepped across a line in a test chamber. Afterwards, the rats were divided and given electrical stimulation either 50 or 150 milliseconds after crossing the line. In addition, the rats differed in terms of the area in which the stimulation electrodes were implanted in their brains (Neutral Area, Area A, or Area B). Researchers were interested in the time it took the animals to re-cross the line on a subsequent learning task. The idea is that stimulation of certain areas in the brain would interfere with memory and hence delay learning to avoid the line on the subsequent learning task. The data on time to re-cross the line are below. What can be concluded with an α of 0.05?

                     Area

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Time: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Area: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Time: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Area: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a time difference in the time it took to step across the line.

There is no time difference in the time it took to step across the line.    

There is an area difference in the time it took to step across the line.

There is no area difference in the time it took to step across the line.    

There is a time by area interaction in the time it took to step across the line.

There is no time by area interaction in the time it took to step across the line.    

Dentists make many people nervous. To see whether such nervousness elevates blood pressure, the blood pressure and pulse rates of 60 subjects were measured in a dental setting and in a medical setting. For each subject, the difference (dental-setting blood pressure minus medical-setting blood pressure) was calculated. The analogous differences were also calculated for pulse rates. Summary data are given below.

(a)

Do the data strongly suggest that true mean blood pressure is greater in a dental setting than in a medical setting? Use a level 0.01 test. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We reject H₀. We do not have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.

We do not reject H₀. We have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.    

We reject H₀. We have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.

We do not reject H₀. We do not have convincing evidence that the mean blood pressure is greater in a dental setting than in a medical setting.

(b)

Is there sufficient evidence to indicate that true mean pulse rate in a dental setting differs from the true mean pulse rate in a medical setting? Use a significance level of 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.

We reject H₀. We do not have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.    

We do not reject H₀. We do not have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.

We reject H₀. We have convincing evidence that the mean pulse rate in a dental setting differs from the mean pulse rate in a medical setting.

Do faculty and students have similar perceptions of what types of behavior are inappropriate in the classroom? This question was examined by the author of an article. Each individual in a random sample of 173 students in general education classes at a large public university was asked to judge various behaviors on a scale from 1 (totally inappropriate) to 5 (totally appropriate). Individuals in a random sample of 98 faculty members also rated the same behaviors.

The mean rating for three of the behaviors studied are shown here (the means are consistent with data provided by the author of the article). The sample standard deviations were not given, but for purposes of this exercise, assume that they are all equal to 1.0.

(a)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to wearing a hat in class differs for students and faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.    

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

(b)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to addressing an instructor by his or her first name is greater for students than for faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.   

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

(c)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to talking on a cell phone differs for students and faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.    

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

(d)

Does the result of the test in part (c) imply that students and faculty consider it acceptable to talk on a cell phone during class?

Yes, the result implies that students and faculty consider it acceptable to talk on a cell phone during class.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that only faculty feel the behavior is appropriate.    

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. However, the sample mean ratings indicate that both groups feel the behavior is appropriate.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that both groups feel the behavior is inappropriate.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that only students feel the behavior is appropriate.

Using both the skew and kurtosis statistics and histograms, determine if there is a significant skew and/or kurtosis for the variables that are appropriate for this analysis. Are they negatively or positively skewed? Justify your answers.

Researchers are interested in the relationship between binge drinking and membership in a Greek life organization on a college campus. Suppose the researchers conduct a thorough questionnaire on a random sample of students and compose the following table displaying their preliminary results. Binge Drinking No Binge Drinking Total Greek Life Organization 131 55 186 No Greek Life Organiation 102 150 252 Total 233 205 438 A) Calculate the prevalence of binge drinking in each of the groups. B) Calculate a prevalence odds ratio for binge drinking based on membership in a Greek life organization.

What is Total repeat rate and give an example of how it would be used?