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# Statistics Problems

1. Classify as independent or dependent samples: The rainfall in the US in two consecutive years.

2. Classify as independent or dependent samples: Average selling price for ten homes in a given neighborhood, and average selling price for ten homes in another neighborhood.

3. The pulse rate of a population of 20 volunteers is tested before and after exercise. In each case, the pulse rates are normally distributed. Can the z test be used to evaluate the difference in the means of each sample? Yes or 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, 6, 1, 6, 7, 8, 8, 9, 10, 7. Assume alpha = 0.05.

i) State the null and alternate hypotheses
ii) Calculate the sample mean and standard deviation
iii) Determine which test statistic is appropriate (z or t), and calculate its value.
iv) Determine the critical value(s).
v) 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 3.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 9, 9, 2, 8, 6, 3, 7, 7, 10, 5, 8, 8, 2, 4, and 9 grams. Assume alpha = 0.10.

i) State the null and alternate hypotheses
ii) Calculate the sample standard deviation
iii) Determine which test statistic is appropriate (chi-square or F), and calculate its value.
iv) Determine the critical value(s).
v) State your decision: Should the null hypothesis be rejected?

6. A telephone survey gives 11 consumers two choices: Do they prefer Coke or Pepsi? Exactly 9 of those surveyed state that they prefer Coke. Assuming that alpha = 0.02, test the hypothesis that the proportion of the population that prefers Coke is 70%.

i) State the null and alternate hypotheses
ii) Calculate the sample proportion
iii) Calculate the value of the test statistic.
iv) Determine the critical value(s).
v) 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 alpha = 0.05, test the hypothesis that the means of the two populations are equal.
i) State the null and alternate hypotheses
ii) Calculate the mean and standard deviation for each group
iii) Calculate the value of the test statistic.
iv) Determine the critical value(s).
v) State your decision: Should the null hypothesis be rejected?

#### Solution Summary

The solution contains detailed step-by step calculations and explanation of the given statistical problems.

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