Unit VI Review
Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees of freedom.
1. 90% confidence interval with df = 4.
Use the t-tables, software, or a calculator to estimate the indicated P-value.
2. P-value for t ≤ 1.76 with 24 degrees of freedom
Interpret the confidence interval.
3. A random sample of clients at a weight loss center were given a dietary supplement to see if it would promote weight loss. The center reported that the 100 clients lost an average of 44 pounds, and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±7 pounds.
Use the given sample data to construct the indicated confidence interval for the population mean.
4. Thirty randomly selected students took the calculus final. If the sample mean was 82 and the standard deviation was 6.0, construct a 99% confidence interval for the mean score of all students.
5. A random sample of 30 long distance runners aged 20-25 was selected from a running club. The resting heart rates (in beats per minute) of the runners are shown below. Estimate the mean resting heart rate for the population of long distance runners aged 20-25. Give the 95% confidence interval.
62 70 61 64 75 54 72 68 74 54
75 70 62 66 79 73 81 60 66 76
67 62 66 69 70 86 76 60 53 71
Determine the margin of error in estimating the population parameter.
6. Based on a sample of size 48, a 95% confidence interval for the mean score of all students on an aptitude test is from 65.3 to 72.7.
Classify the hypothesis test as lower-tailed, upper-tailed, or two-sided.
7. A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.
For the given hypothesis test, explain the meaning of a Type I error or a Type II error, as specified.
8. In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:
H0 : μ = 8.0 hours
HA : μ > 8.0 hours
Explain the result of a Type II error.
Use a hypothesis test to test the given claim.
9. Is the mean weight of female college students still 132 pounds? To test this, you take a random sample of 20 students, finding a mean of 137 pounds with a standard deviation of 14.2 pounds. Use a significance level of 0.1.
Provide an appropriate response.
10. You want to determine if the average gas price in your city has exceeded $2.15 per gallon for regular gas. You take a random sample of prices from 8 gas stations, recording the following prices: $2.13, $2.10, $1.80, $2.09, $2.17, $2.12, $2.10, $2.11. Have the conditions and assumptions for inference been met?
11. Suppose you have obtained a confidence interval for μ, but wish to obtain a greater degree of precision. Which of the following would result in a narrower confidence interval?
A. Increasing the sample size while keeping the confidence level fixed
B. Decreasing the sample size while keeping the confidence level fixed
C. Increasing the confidence level while keeping the sample size fixed
D. Decreasing the confidence level while keeping the sample size fixed
Construct the indicated confidence interval for the difference between the two population means. Assume that the assumptions and conditions for inference have been met.
12. A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 99% confidence interval for μ1 - μ 2 where μ1 and μ2 represent the mean for the treatment group and the control group respectively.
Treatment Group Control Group n1 = 85