Statistic worksheet

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Name:______________________________________ Module 2 Homework Assignment 1.) 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours. Solution: 2.) Instructor Comments: Find the critical value for zα/2 that corresponds to a degree of confidence of 98%. Solution: Instructor Comments: 3.) Find the critical value for tα/2 corresponding to n = 12 and 95% confidence level. Solution: Instructor Comments: 4.) Use the confidence level and sample data to find the margin of error E. College students’ annual earnings: 99% confidence, n = 74, x = $3967, s = $874 Solution: Instructor Comments: 5.) Construct the confidence interval for question 4 above. Solution: Instructor Comments: 6.) Write a statement that correctly interprets the confidence interval found in question 5. Solution: Instructor Comments: 7.) Find the critical value  L2 corresponding to a sample size of 19 and a confidence level of 99% if the test is two-tailed. Solution: Instructor Comments: Find the critical value  R2 corresponding to a sample size of 19 and a confidence level of 99% if 8.) the test is two-tailed. Solution: Instructor Comments: 9.) The values listed below are the waiting times (in minutes) of customers at the Bank of Providence, where customers enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation  and write a statement that correctly interprets the results. 4.2 Solution: 5.4 5.8 6.2 6.7 7.7 8.5 9.3 10.0 Instructor Comments: 10.) You want to estimate  for the population of waiting times at a fast-food restaurant’s drive-up windows, and you want to be 95% confident that the sample standard deviation is within 20% of . Find the minimum sample size needed. Is this sample size practical? Solution: Instructor Comments: Name:______________________________________ Module 3 Homework Assignment 1. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution or neither. The sample data appear to come from a normally distributed population with σ = 28. Explain. Claim: μ = 977. Sample data: n = 25, 𝑥̅ = 984, s = 25. Explain. Solution: Instructor Comments: 2. In a sample of 100 M&M’s, it is found that 8% are brown. Use a 0.05 significance level to test the claim that of the Mars candy company that the percentage of brown M&M’s is equal to 13%. Identify the null and alternative hypotheses. Solution: Instructor Comments: 3. (Refer to problem 2) Find the test statistic. Solution: Instructor Comments: 4. (Refer to problem 2) Use the Standard Normal Table to find the p-value, critical value(s) and state the decision about the null hypothesis. Solution: Instructor Comments: 5. (Refer to problem 2) State the conclusion in non-technical terms. Solution: Instructor Comments: 6. Test the claim that for the adult population of one town, the mean annual salary is given by μ = 30,000. Sample data are summarized as n = 17, x = $22,298, and s = $14,200. Use a significance level of α = 0.05. State the null and alternative hypotheses. Solution: Instructor Comments: 7. (Refer to Question 6) Find the test statistic. Solution: Instructor Comments: 8. (Refer to Question 6) Find the critical value(s) and state decision about null hypothesis. Solution: Instructor Comments: 9. (Refer to Question 6) State the conclusion in non-technical terms. Solution: Instructor Comments: 10. Find the critical value or values of χ2 based on the given information. H1: σ > 26.1, n = 9, α = 0.01 Solution: Instructor Comments:
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Name:______________________________________

Module 3 Homework Assignment
1. Determine whether the hypothesis test involves a sampling distribution of means that is a normal
distribution, Student t distribution or neither. The sample data appear to come from a normally
distributed population with σ = 28. Explain.
Claim: μ = 977.
Sample data: n = 25, 𝑥̅ = 984, s = 25. Explain.
Solution:

Instructor Comments:

1. Here we are given, the sample data appear
to come from a normally distributed
population with σ = 28.
The hypothesis test involves normal
distribution.

2. In a sample of 100 M&M’s, it is found that 8% are brown. Use a 0.05 significance level to test the
claim that of the Mars candy company that the percentage of brown M&M’s is equal to 13%. Identify
the nu...


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