Kevin retired on 1/1/2020 and started to withdraw $2500 at the end of each month from an account (which earns 2.35% interest compounded monthly) containing $439,979.16. If Kevin keeps on making the set withdrawal and the interest rate remains the same, then the account should last for ___ years. The total interest that Kevin earns from the account (from the time that he starts withdrawing the $2500 to the very last withdrawl that he makes) would be $____.

Which of the given is not a requirement for the validity of the chi‑square goodness‑of‑fit test?

1) independent observations

2) all observations falling into one of k outcome classes

3) a fixed number of observations

4) normally distributed data

10. The grades of students are normal distributed. In a class of 10 students the average grade on a quiz is 16.35, with a standard deviation of 4.15. ( 3 marks ) a) Find the 90% confidence interval for the population mean grade. b) If you wanted a wider confidence interval, would you increase or decrease the confidence level?

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. (Change the final answer to a % and keep 2 decimal places) a) Find the probability that a randomly selected TV set will have a replacement time between 9.5 and 10.5 years. (Include diagram) b) Find the probability that 35 randomly selected TV sets will have a mean replacement time less than 8.0 years. (Include diagram)

At a local college, 65 female students were randomly selected and it was found that their mean monthly income
was $609. Seventy-five male students were also randomly selected and their mean monthly income was found to
be $651. Test the claim that male students have a higher monthly income than female students. Assume the
population standard deviation for the females is $121.50 and for the males $131. Use α = 0.01

A story spoiler gives away the ending early. Does having a story spoiled in this way diminish suspense and hurt enjoyment? A study¹ investigated this question. For twelve different short stories, the study’s authors created a second version in which a spoiler paragraph at the beginning discussed the story and revealed the outcome. Each version of the twelve stories was read by at least 30 people and rated on a 1 to 10 scale to create an overall rating for the story, with higher ratings indicating greater enjoyment of the story. The ratings are given in Table 1 and stored in StorySpoilers. Stories 1 to 4 were ironic twist stories, stories 5 to 8 were mysteries, and stories 9 to 12 were literary stories. Test to see if there is a difference in mean overall enjoyment rating based on whether or not there is a spoiler.

Table 1 Enjoyment ratings for stories with and without spoilers

Find a 95% confidence interval for the difference in mean enjoyment rating between stories with a spoiler and stories without.

Click here for the dataset associated with this question.

Round your answers to three decimal places.

The 95% confidence interval is.....??????????

1. using the following data set, write a null hypothesis. Record both a generic version (through the use symbols) and an English version (using words) – for the generic version.

2. Compose an alternative hypothesis to accompany the test. Record both a generic version (through the use of symbols) and an English version (using words) – for the generic version.

3. What type of test should be used?

4. Interpret the results.

A genetic experiment with peas resulted in one sample of offspring that consisted of 404 green peas and 161

yellow peas.

a. Construct a 95​% confidence interval to estimate of the percentage of yellow peas.

b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

a. Construct a 95​% confidence interval. Express the percentages in decimal form.

? < p < ?

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

b. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%

​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

The following data set represents the final grades assigned in a statistics course. The grades are as followed, 60, 50, 85, 85, 85, 90, 100, 70, 83, 92, 68, 70, 88, 88, 85, 90, 20, 100, 90, 80, 77

1. Professor Williamson believes that the average grade she would assign would be an 85. Is she correct?

2. Determine an appropriate alpha level for the given data set and justify your reason

3. Create your null and alternate hypothesis

4. Perform a hypothesis test from the sample data

5. What is your t-value?

6. What is your critical T-value?

7. What is your estimated P-value or exact P-value?

8. Draw a normal curve of distribution that depicts your critical t-value, t-value and your P-value. Shade the graph where appropriate.

9. What is the general rule for all hypothesis testing when comparing p-values to alpha values?

10. Determine the conclusion of your data set using statistical language.

11. interpret your results of the data set based on the content of the question.

12. According to the Central limit theorem, the larger your sample size gets, something will happen to your data set. How does this affect hypothesis testing? Does this affect any type I or type II errors that could occur?

13. According to your results from this question, what conclusions can you make about the sample mean and Professor Williamson’s average?

Problem 1: A new program of imagery training is used to improve the performance of basketball players shooting free-throw shots. The first group did an hour imagery practice, and then shot 30 free throw basket shots with the number of shots made recorded. A second group
received no special practice, and also shot 30 free throw basket shots. The data are
below. Did the imagery training make a difference? Set alpha = .05.

Group 1: 15, 17, 20, 25 26, 27

Group 2: 5, 6, 10, 15, 18, 20

1. You must use all five steps in hypothesis testing:

1. Restate the question as a research hypothesis and a null hypothesis about the populations.
2. Determine the characteristics of the comparison distribution.
3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
4. Determine your sample’s score on the comparison distribution.
5. Decide whether to reject the null hypothesis.

2. Solve for and evaluate the effect size of this study using Cohen's D.

3. Create a 90% confidence interval for this problem.

In a test of a new medication, 65 out of 98 males and 45 out of 85 females responded positively. At the 0.05 level of significance, can we say that the drug is more effective for males?

What is the probability that if a pair of dice is rolled eighteen times, exactly three sums of seven are rolled? (Round your answer to four decimal places.)

A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 2.2. (Round your answers to two decimal places.)

(a) Compute a 95% CI for μ when n = 25 and x = 54.9

(         ,         )watts

(b) Compute a 95% CI for μ when n = 100 and x = 54.9.

(c) Compute a 99% CI for μ when n = 100 and x = 54.9.

(         ,       )watts

(d) Compute an 82% CI for μ when n = 100 and x = 54.9.

(     ,     )watts

(e) How large must n be if the width of the 99% interval for μ is to be 1.0? (Round your answer up to the nearest whole number.)
n =

Slot machines are the favorite game at casinos throughout the United States (Harrah’s Survey 2002: Profile of the American Gambler). A local casino wants to estimate the difference in the percent of women and me who prefer the slots with a 95% level of confidence. Random samples of 320 women and 250 men found that 256 women prefer slots and 165 men prefer slots.

1-

-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

The National Endowment for the Humanities sponsors summer institutes to improve the skills of high school language teachers. One institute hosted 20 French teachers for four weeks. At the beginning of the period, the teachers took the Modern Language Association's listening test of understanding of spoken French. After four weeks of immersion in French in and out of class, they took the listening test again. (The actual spoken French in the two tests was different, so that simply taking the first test should not improve the score on the second test.) The Director of the summer institute would like to estimate the change (and hopeful improvement) in the teachers' skills after participating in the class.

1-

-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions