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# Classify as independent or dependent samples: Average pulse rate of ten runners before a race, and average pulse rate of those ten runners after a...

1. Classify as independent or dependent samples: Average pulse rate of ten runners before a race, and average pulse rate of those ten runners after a race.
independent
dependent

2. Classify as independent or dependent samples: The effectiveness of Tylenol on twenty patients, and the effectiveness of aspirin on those twenty patients.
independent
dependent

3. An aerospace parts factory has one production line creating a single population of fasteners; the widths of these fasteners are normally distributed. A sample of 20 fasteners is selected from the production line for quality control inspection. The width of each selected fastener is measured; and the mean of the measured widths of selected fasteners is compared to the design value. Can the z test be used in this hypothesis test?
Yes
No

4. The US Mint selects ten pennies from the production line to test the hypothesis that the mean weight of each penny is 4 grams. The normally-distributed weights (in grams) of these pennies are as follows: 7, 3, 8, 5, 9, 9, 5, 5, 3, 5. Assume squiggley a = 0.05.
•?State the null and alternate hypotheses
•?Calculate the sample mean and standard deviation
•?Determine which test statistic is appropriate (z or t), and calculate its value.
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?

5. A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 8, 9, 4, 6, 9, 6, 3, 1, 10, 3, 7, 10, 7, 5, and 6 grams. Assume squiggley a = 0.10.
•?State the null and alternate hypotheses
•?Calculate the sample standard deviation
•?Determine which test statistic is appropriate (chi-square or F), and calculate its value.
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?

6. A telephone survey gives 601 consumers two choices: Do they prefer Coke or Pepsi? Exactly 248 of those surveyed state that they prefer Coke. Assuming that squiggley a = 0.02, test the hypothesis that the proportion of the population that prefers Coke is 70%.
•?State the null and alternate hypotheses
•?Calculate the sample proportion
•?Calculate the value of the test statistic.
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?

7. Two groups of ten sprinters run 100 meters. The times required by sprinters in the first group are as follows:
10.8 11.1 10.5 11.8 10.3 10.4 10.4 12.9 10.1 14.3
The times required by sprinters in the second group are as follows:
14.0 18.0 19.8 18.3 13.5 10.6 16.4 17.5 19.4 16.2
Assuming that = 0.05, test the hypothesis that the means of the two populations are equal.
•?State the null and alternate hypotheses
•?Calculate the mean and standard deviation for each group
•?Calculate the value of the test statistic.
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?

8. A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
2.97 2.86 2.82 2.86 2.95 2.80 2.81 2.98 2.88 2.83 2.95 2.95
Assuming that squggley a = 0.01, test the hypothesis that the population mean is equal to 3.
•?State the null and alternate hypotheses
•?Calculate the mean and standard deviation
•?Determine which test statistic applies, and calculate it
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?

9. A sample of size n = 20 is selected from a normal population to construct a 90% confidence interval estimate for a population mean. The interval was computed to be (7.60 to 10.70). Determine the sample standard deviation.

10. A random sample of 41 observations was selected from a normally distributed population. The sample mean was xbar= 60, and the sample variance was s ^2 = 21.0. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 6 at the 0.05 level of significance? Use the p-value method.
•?State the null and alternate hypotheses
•?Determine which test statistic applies, and calculate it
•?Determine the corresponding probability, and compare to (squggley a)
•?State your decision: Should the null hypothesis be rejected?

11. An insurance company states that 75% of its claims are settled within 5 weeks. A consumer group selected a random sample of 65 of the company's claims and found 43 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group's claim that fewer than 75% of the claims were settled within 5 weeks? Test using the traditional approach with a = 0.05.
•?State the null and alternate hypotheses
•?Calculate the sample proportion
•?Determine which test statistic applies, and calculate it
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?

12. A teacher wishes to compare two different groups of students with respect to their mean time to complete a standardized test. The time required is determined for each group. The data summary is given below. Test the claim at squiggley a = 0.10, that there is no difference in variance. Give the critical region, test statistic value, and conclusion for the F test.
n1 = 24 s1 = 21
n2 = 40 s2 = 39
squiggley a = 0.10
•?State the null and alternate hypotheses
•?Determine which test statistic applies, and calculate it
•?Determine the critical region
•?State your decision: Should the null hypothesis be rejected?

13. A machine produces 9 inch latex gloves. A sample of 48 gloves is selected, and it is found that 27 are shorter than they should be. Find the 99% confidence interval on the proportion of all such gloves that are shorter than 9 inches.

14. The pulse rates below were recorded over a 30-second time period, both before and after a physical fitness regimen. The data is shown below for 8 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume pulse rates are normally distributed. Test using that sign that looks like a = 0.05.
•?State the null and alternate hypotheses
•?Calculate the mean and standard deviation
•?Determine which test statistic applies, and calculate it
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?
Before 51 31 33 44 39 48 40 54
After 46 35 48 50 32 52 59 48

15. You are given the following data. Test the claim that there is a difference in the means of the two groups. Use = 0.05.
Group A Group B
xbar1 = 2 xbar2= 5
s1= 19 s2= 18
n1= 31 n2= 49
•?State the null and alternate hypotheses
•?Determine which test statistic applies, and calculate it
•?Determine the critical value(s).
•?State your decision: Should the null hypothesis be rejected?
1.   Classify as independent or dependent samples: Average pulse rate of ten runners before a race, and average pulse rate of those ten runners after a race.           independent           dependent   2.   Classify as independent or dependent samples: The effectiveness of Tylenol on twenty patients, and the effectiveness of aspirin on those twenty patients.           independent           dependent   3.   An aerospace parts factory has one production line creating a single population of fasteners; the widths of these fasteners are normally distributed. A sample of 20 fasteners is selected from the production line for quality control inspection. The width of each selected fastener is measured; and the mean of the measured widths of selected fasteners is compared to the design value. Can the z test be used in this hypothesis test?           Yes           No   4.   The US Mint selects ten pennies from the production line to test the hypothesis that the mean weight of each penny is 4 grams. The normally-distributed weights (in grams) of these pennies are as follows: 7, 3, 8, 5, 9, 9, 5, 5, 3, 5. Assume = 0.05. State the null and alternate hypotheses Calculate the sample mean and standard deviation Determine which test statistic is appropriate (z or t), and calculate its value. Determine the critical value(s). State your decision: Should the null hypothesis be rejected? 5.   A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 8, 9, 4, 6, 9, 6, 3,
1, 10, 3, 7, 10, 7, 5, and 6 grams. Assume a = 0.10. State the null and alternate hypotheses Calculate the sample standard deviation Determine which test statistic is appropriate (chi-square or F), and calculate its value. Determine the critical value(s). State your decision: Should the null hypothesis be rejected? 6.   A telephone survey gives 601 consumers two choices: Do they prefer Coke or Pepsi? Exactly 248 of those surveyed state that they prefer Coke. Assuming that      = 0.02, test the hypothesis that the proportion of the population that prefers Coke is 70%. State the null and alternate hypotheses Calculate the sample proportion Calculate the value of the test statistic. Determine the critical value(s). State your decision: Should the null hypothesis be rejected? 7.   Two groups of ten sprinters run 100 meters. The times required by sprinters in the first group are as follows: 10.8 11.1 10.5 11.8 10.3 10.4 10.4 12.9 10.1 14.3 The times required by sprinters in the second group are as follows: 14.0 18.0 19.8 18.3 13.5 10.6 16.4 17.5 19.4 16.2 Assuming that = 0.05, test the hypothesis that the means of the two populations are equal. State the null and alternate hypotheses Calculate the mean and standard deviation for each group Calculate the value of the test statistic. Determine the critical value(s). State your decision: Should the null hypothesis be rejected? 8. A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows: 2.97 2.86 2.82 2.86 2.95 2.80 2.81 2.98 2.88 2.83 2.95 2.95 Assuming that = 0.01, test the hypothesis that the population mean is equal to 3. State the null and alternate hypotheses Calculate the mean and standard deviation Determine which test statistic applies, and calculate it Determine the critical value(s).
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