A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below. Age Group Watch 11 p.m. News? 18 or less 19 to 35 36 to 54 55 or Older Total Yes 42 57 61 82 242 No 208 193 189 168 758 Total 250 250 250 250 1,000 (a) Let p1, p2, p3, and p4 be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H0 that p1, p2, p3, and p4 are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.) χ2χ2 = so (Click to select)Do not rejectReject H0: independence (b) Compute a 95 percent confidence interval for the difference between p1 and p4. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% CI: [ , ]

In 1950​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1100 adults​ surveyed, 363 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 319 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol​ changed? Use the α = 0.01 level of significance. Normality criteria have been satisfied.

Write the Null and Alternative Hypothesis:

Give the Test statistic and P value:

State the conclusion in context:

When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and “Alternate” hypotheses, ii. S2: manually calculate value of the test statistic, iii. S3: specify the level of significance and the critical value of the statistic, iv. S5: use appropriate decision rule and then reach a conclusion about not rejecting or rejecting the null hypothesis. S5: If asked to calculate p–value,do so and relate the p-value to the level of significance in reaching your conclusion. If you use MiniTab to perform the hypothesis test, you must paste the relevant output into your assignment. This output simply verifies and occasionally replaces the manual computation of the test statistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, to make your testing procedure standard and complete. If Confidence Coefficient (CC) and Level of Significance (LS) are not specified, assume the default values of 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) and no more or no less, when calculations are done with a calculator.

Sample_BMI

34.74
31.95
30.34
16.79
38.57
33.55
25.29
26.70
26.49
30.98
22.12
22.28
29.73
33.18
25.63
20.78
24.14
29.35
26.15
23.56
30.45
28.49
22.35
28.58
22.11

Test the hypothesis that the population median of the BMI is other than 29.50. Also, find the 95% Confidence Interval for this population median. Is it consistent?

Please use Minitab to show your work and tell me the steps in Minitab

We have learned hypothesis tests

1. for the mean (when population variance is known and when it is unknown)
2. for a percentage
3. to see if the means of two sets of data are the same
4. goodness of fit test
5. test for independence

For each type give a brief example. You do not have to solve the problem you give. Try to come up with a problem on your own

ou wish to determine if there is a negative linear correlation between the age of a driver and the number of driver deaths. The following table represents the age of a driver and the number of driver deaths per 100,000. Use a significance level of 0.05 and round all values to 4 decimal places.

Ho: ρ = 0
Ha: ρ < 0

Find the Linear Correlation Coefficient
r =

Find the p-value
p-value =

The p-value is

• Less than (or equal to) αα
• Greater than αα

The p-value leads to a decision to

• Reject Ho
• Accept Ho
• Do Not Reject Ho

The conclusion is

• There is a significant linear correlation between driver age and number of driver deaths.
• There is a significant negative linear correlation between driver age and number of driver deaths.
• There is a significant positive linear correlation between driver age and number of driver deaths.
• There is insufficient evidence to make a conclusion about the linear correlation between driver age and number of driver deaths.

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.301.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.498.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent chi-square distributions. We have random samples from each population.The populations follow independent normal distributions.    The populations follow independent normal distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.2000.100 < p-value < 0.200    0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.    Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Measurements on the percentage of enrichment of 12 fuel rods used in a nuclear reactor were reported in the data below. Assume the population of interest is normally distributed

A. Test the hypotheses H0 : µ = 2.95 vs. H1 : µ > 2.95 at the 0.01 significance level. provide a copy of your R input and output, state your conclusion in context

B. Find and interpret the lower 99% confidence bound on the true mean percentage of enrichment. use the interval from your R output

DATA:

(%)

3.11

2.88

3.08

3.01

2.84

2.86

3.04

3.09

3.08

2.89

3.12

2.98

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are the same.H₀: The distributions are different.
H₁: The distributions are different.    H₀: The distributions are the same.
H₁: The distributions are different.H₀: The distributions are the same.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


Are all the expected frequencies greater than 5?

Yes or No    

What sampling distribution will you use?

uniformbinomial    Student's tnormalchi-square

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.    

Share the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Define the population parameter, the appropriate test statistic formula, and if it is a one- or two-tailed test. Be sure to set up your hypotheses, too.

The two population parameters that we cover this week are:

μ: the population mean

and

p: the population proportion

Be sure to include numerical values for your variables. Additionally, identify the Type I and Type II Errors that could occur with your decision‐making process.

Can you please show both in RStudio code? Thank You

Airports:

The temperature is recorded at 60 airports in a region. The average temperature is 68 degrees Fahrenheit with a standard deviation of 5 degrees. The last known average temperature from all airports is 67 degrees Fahrenheit.   Is the recorded temperature at the 60 airports different from the average temperature at all airports?

• Answer by determining statistical significance using the test statistic, degrees of freedom, and p-value.
• Answer substantive significance with difference in means and effect size.

New York Attitudes:

The New York Chamber of Commerce has asked you to do a study concerning people's attitudes toward our city. As part of the study, you will ask them to rate their image of New York on a scale from 1 to 100 (1= awful city - call in the bulldozers; 100 = wonderful city - there is none better). Previous data show this scale is normally distributed with a last known population average rating of 50 and a standard deviation of 10.

Consider the following data for a dependent variable y and two independent variables, x₁ and x₂.

The estimated regression equation for these data is

ŷ = −18.52 + 2.01x₁ + 4.75x₂.

Here, SST = 15,234.1, SSR = 14,109.8, s_b1 = 0.2464, and s_b2 = 0.9457.

(a)Test for a significant relationship among x₁, x₂, and y. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = β₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: β₁ < β₂
H_a: β₁ ≥ β₂    H₀: β₁ ≠ 0 and β₂ = 0
H_a: β₁ = 0 and β₂ ≠ 0H₀: β₁ > β₂
H_a: β₁ ≤ β₂H₀: β₁ ≠ 0 and β₂ ≠ 0
H_a: One or more of the parameters is equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.    Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(b)Is β₁ significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ < 0
H_a: β₁ ≥ 0    H₀: β₁ = 0
H_a: β₁ > 0H₀: β₁ > 0
H_a: β₁ ≤ 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that β₁ is significant.Reject H₀. There is insufficient evidence to conclude that β₁ is significant.    Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(c)Is β₂ significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₂ ≠ 0
H_a: β₂ = 0H₀: β₂ > 0
H_a: β₂ ≤ 0    H₀: β₂ = 0
H_a: β₂ ≠ 0H₀: β₂ = 0
H_a: β₂ > 0H₀: β₂ < 0
H_a: β₂ ≥ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Reject H₀. There is sufficient evidence to conclude that β₂ is significant.    

Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.

A Mission college administrator claims the population mean for student’s commute time is 30 minutes. A sample of 144 Mission College students shows a sample mean commute time = 32 minutes with sample standard deviation s = 12 minutes. Can you show at 99% confidence that the administrator’s claim is wrong? Before doing the problem, you must show that the problem meets the requirements for performing the test. Be sure to show your null and alternate hypothesis, show your test statistic and critical region, and state your conclusion clearly: could the administrator’s claim be true?   YES or   NO

Please show steps in Ti84 calculator, if applicabl

Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μμ = 125 mg/dl and σσ = 15 mg/dl.

(a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes?
(b) If measurements are made on 7 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

Andrew plans to retire in 36 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
(b) What is the probability that the mean return will be less than 4%?

(1) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 65 professional actors, it was found that 37 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) ____

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit ____

upper limit ____

(2) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 610 potsherds was found, of which 365 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.) ____


(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

(3) What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.34 ____


(b) there is no preliminary estimate for p ____