An elementary principal is interested in determining if pulling 5^th and 6^th grade students out of class to participate in music classes (e.g., orchestra, band, choir) has a significant impact on their course grades. Twenty students from the two grades miss math class once per week due to music. The average grade for math class among all students is 80%. Do these music students have significantly different grades than the rest of the students (m=80, s=8). Test at the .01 level. (15 pts total)

Z-test results:
m - mean of Variable (Std. Dev. = 8)
H₀ : m=80
H_A : m not equal 80

Step 1: Develop Hypotheses:

a.     Independent Variable =                                                       Scale: Categorical Quantitative (1.5 pts)

b.    Dependent Variable =                                                         Scale: Categorical       Quantitative         (1.5 pts)

c.     Circle:     One-tailed       Two-tailed (.05 pt)

d.    Alternative hypothesis in sentence form (1 pt).                                                                                                                                                  

e.     Null hypothesis in sentence form (1 pt).                                                                                                                

f.     Write the alternative and null hypotheses using correct notation (2 pts).

                                                     H₁:                                                                H₀:                                                                                                                         

Step 2: Establish significance criteria (.05 pt)

g.     a =

Step 3: Calculate test statistic, effect size, confidence interval

h.    z_calculated =                                                           Level of significance (p) =                                                                   (1 pt)                         

i.     Decision:      reject null     or                   fail to reject null                                                 (1 pt)

j.     Calculate effect size =                                                                                                                                                        (2 pts)                                                                                                                               

Step 4: Draw conclusion

k.    Write your conclusion in sentence form including appropriate results notation (3 pts).

The average American consumes 80 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 12 randomly selected college students and found that they averaged 97.6 liters of alcohol consumed per year with a standard deviation of 23 liters. What can be concluded at the the αα = 0.01 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  Select an answer ≠ = > <       

H1:H1:  ? p μ  Select an answer > < = ≠    

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean amount of alcohol consumed by college students is not significantly more than 80 liters per year at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 80 liters per year.
   • The data suggest the population mean is not significantly more than 80 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is equal to 80 liters per year.
   • The data suggest the populaton mean is significantly more than 80 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 80 liters per year.

1.    A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 200 students is obtained, and each student is given a standardized verbal test and a standardized math test. Based on the test results, students are classified as high or low for verbal skills and for math skills. The results are summarized in the following frequency distribution:  

                                                          Verbal Skills

                                   High                        Low

Test at the .05 level of significance whether there is a significant relationship between verbal skills and math skills.

df = __________

Χ² = ________

CV = _________

Is there a significant relationship between verbal skills and math skills? a. YES b. NO

Choose the best report:

a. There is a consistent predictable relationship between verbal skills and math skills for high school students, n = 200, df 1 X² = 15.84.

b. There is a significant difference between verbal skills and math skills; X² (2, n=200) = 15.84, p < .05.

c. There is a significant relationship between verbal and math skills X² (1, n=200) = 15.84, p < .05.

d. We retain the null, that there is no relationship between verbal skill and math skills for high school students. The X²= 0.5 with a CV (1) = 3.841. There is no effect because we retained the null. But if you were to calculate it, it would be = 0.05.

e. While running a basic analysis test, it was found that there is significant relationship skills between verbal skills and math skills. With a X² = 17.68 and utilizing 1 df, the cv = 3.841.

The upcoming championship high school football game is a big deal in your little town. The problem is, it is being played in the next biggest town, which is two hours away! To get as many people as you can to attend the game, you decide to come up with a ride-sharing app, but you want to be sure it will be used before you put all the time in to creating it. You determine that if more than three students share a ride, on average, you will create the app.

You conduct simple random sampling of 20 students in a school with a population of 300 students to determine how many students are in each ride-share (carpool) on the way to school every day to get a good idea of who would use the app. The following data are collected:

• 6 5 5 5 3 2 3 6 2 2
• 5 4 3 3 4 2 5 3 4 5

You and your partner will construct a 90% confidence interval and 95% confidence interval for the mean number of students who share a ride to school, then you will compare and interpret the results.

Part A: Decide which partner will construct each confidence interval, and then state the parameter and check the conditions. (Individual work)

Part B: Construct the confidence interval. Be sure to show all your work, including the degrees of freedom, critical value, sample statistics, and an explanation of your process. (Individual work)

Part C: Interpret, share, and compare. Interpret the meaning of the confidence interval, compare your results with your partner, and describe the difference in the width of the interval and the margin of error. (Collaborative work)

Part D: Use your findings to explain whether you should develop the ride-share app for the football game.

Now generate at least 5000 bootstrap samples and observe the bootstrap distribution.a.What does each dot in the distribution represent?b.Where is the middle of the distribution?c.What is the standard error for the distribution?d.Use the standard errorto compute a 95% confidence interval for the correlation.e.Now use the percentile method to compute a 95% confidence interval. (remember, click on the ‘Two-Tail’ box in the distribution plot). Are the two 95% confidence intervalsvery different?5.Using the confidence interval from part 4 (either one), can we claim that there is an association between car price and depreciation? Hint: An association would mean the population correlation is not zero –we can only claim association if zero is nota possible value for rho. 6.Would you answer to part 5 change if we built a 99% confidence interval? Hint: Does the interval get wider or narrow when we go to 99%.Does this change whether or not 0 is included in the interval?Activity 3: Are female students more likely to smoke than male students?Still in StatKey, go to bootstrap CI for a difference inproportions. We are going to use data from a sample of 169 female students and 193 male students. Each participant was asked whether or not she or he smoked. Our task is to build confidence intervals for the difference in proportion of students who smoke when comparing females to males. Select the Data set ‘Student Survey: Smoke by Gender?’.1.What arethe sample sizes?2.What is the value and notation for the sample statistic?3.Find a 90% confidence interval using at least 5000 bootstrap statistics. 4.Using your answerfrom question 3:a.At 90% confidence, can we claim that there is a difference in the proportion of smokers when comparing females to males?b.What about at 99% confidence?

Question 1: (1 point)

Identify the independent and dependent variables in each example below.

Environmentalists have a theory that as smoke-stack and tailpipe emissions have increased over the past centuries, global warming has occurred.

An educational researcher is interested in effects of nutrition on school performance. She classifies students as breakfast eaters and non-breakfast eaters. She measures school performance by recording school attendance rate.

Question 2: (2points)

At what level of measurement is the following data and what type of graph can be used?

SAT scores of students collected from a sample of students in Berkeley College.

A meteorologist classifies cities in the US as having winter weather as dreary, not dreary.

A kindergarten teacher classifies students as readers, incipient readers, nonreaders.

A housing developer advertises his houses as being fully carpeted, partially carpeted or not carpeted

Question 3: (2 points)

The college registrar is asked to count the number of usable chairs in different classrooms at her university to determine how many students can be seated in each class. These are number of usable chairs in the different classrooms:

7, 12, 26, 18, 20, 33, 34, 17, 20, 35, 46, 50, 28, 29, 33, 18, 45, 53, 30, 37, 45, 58, 43, 42, 10, 34, 28, 35, 36, 50, 60, 55, 45, 52, 54, 28, 34, 25, 35, 40, 45, 44, 40, 23, 38, 39, 40, 50, 60, 45, 36, 28, 40, 54, 62, 44, 24, 28, 30, 60, 38, 58, 24.

At what level of measurement is this data & what type of graph is appropriate?

Make steam-and-leaf display

Describe modality & symmetry (skewness) of this data

In​ 1996, 61​% of high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. A recent survey found that 236 of 400 high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. Do high school teachers feel differently today than they did in​ 1996? ​(a) What does it mean to make a Type II error for this​ test? ​(b) If the researcher decides to test this hypothesis at the alphaequals0.10 level of​ significance, compute the probability of making a Type II​ error, beta​, if the true population proportion is 0.59. What is the power of the​ test? ​(c) Redo part​ (b) if the true population proportion is 0.56. ​(a) What does it mean to make a Type II error for this​ test? Choose the correct answer below. A. Upper H 0 is not rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is not equal to 0.61. B. Upper H 0 is not rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is equal to 0.61. C. Upper H 0 is rejected and the true proportion of high school teachers who believe that students are not attentive in the classroom is not equal to 0.61. ​(b) If the researcher decides to test this hypothesis at the alphaequals0.10 level of​ significance, compute the probability of making a Type II​ error, beta​, if the true population proportion is 0.59. What is the power of the​ test? beta equals nothing Power equals nothing ​(Type integers or decimals rounded to four decimal places as​ needed.) ​(c) Redo part​ (b) if the true population proportion is 0.56. beta equals nothing Power equals nothing ​(Type integers or decimals rounded to four decimal places as​ needed.)

Kenton and Denton Universities offer executive training courses to corporate clients. Kenton pays its instructors $5,000 per course taught. Denton pays its instructors $250 per student enrolled in the class. Both universities charge executives a $450 tuition fee per course attended.

Required

Prepare income statements for Kenton and Denton, assuming that 20 students attend a course.

Kenton University embarks on a strategy to entice students from Denton University by lowering its tuition to $240 per course. Prepare an income statement for Kenton assuming that the university is successful and enrolls 40 students in its course.

Denton University embarks on a strategy to entice students from Kenton University by lowering its tuition to $240 per course. Prepare an income statement for Denton, assuming that the university is successful and enrolls 40 students in its course.

Problem 11-28

a.      N = Number of units to break-even point

Sales − Variable cost − Fixed cost = Desired Profit

          (Sales price x N) − (Variable cost per unit x N) = Fixed cost + Desired Profit

(Contribution margin per unit x N) = Fixed cost + Desired Profit

N = (Fixed cost + Desired Profit) ÷ Contribution margin per unit

N = ($               + $           ) ÷ [$       - ($     + $       )] =          Units

          Break-even point dollars =        Units x $        selling price per unit = $

b.      N = Number of units to break-even point

          N = (Fixed cost + Desired Profit) ÷ Contribution margin per unit

          N = ($            + $            ) ÷ [$        – ($       + $      )]

          N =          Units

          Break-even point dollars =    Units x $            selling price per unit = $

I'm struggling with writing null and alternative hypothesis for two populations. Can anyone please explain HOW TO write the correct Ho and Ha for the following questions? Thanks.

Examples:

1) Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

2) A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.

3) A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3.

A. A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following results. The mean GPA for college A was x1 = 3.11, with a standard deviation s1 = 0.44. The GPA for college B was 2 = 3.44, with a standard deviation s2 = 0.55. Determine a 95% confidence interval for the difference, µ1-µ2 between the mean GPA of college A students and the mean GPA of college B students. (Assume college a and B have the same population standard deviations)

B. A manufacturing process produces bags of cookies. The distribution of content weights of these bags is Normal with mean 15.0 oz and standard deviation 6.0 oz. We will randomly select a sample of 900 bags of cookies and weigh the contents of each bag selected, is the mean of such sample

a) The mean of is x

b) The standard deviation of x is

c) The distribution of x is

d) Does the distribution of depend on the assumption that the weight (in oz) of these bags is normally distributed and why?

C.Last year, the mean annual salary for adults in one town was $35,000. A researcher wants to perform a hypothesis test to determine whether the mean annual salary for adults in this town has changed this year. The mean annual salary for a random sample of 16 adults from the town was 33000. Assume population standard deviation σ =12000. Use a significance level of α=0.05

D. A special diet is intended to reduce the cholesterol of patients at risk of heart disease. After six months on the diet, an SRS of 64 patients at risk for heart disease had an average cholesterol of x= 192, with standard deviation s = 24. The 95% confidence interval for the average cholesterol of patients at risk for heart disease who have been on the diet for 6 months is