# Independent or Dependent Samples, Z-test, Critical Value

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1. Classify as independent or dependent samples: The average price of gasoline at ten local stations, and the average price of gasoline at ten stations in another state.

independent

dependent

2. Classify as independent or dependent samples: The number of crimes committed in Pittsburgh, and the number of crimes committed in Los Angeles.

independent

dependent

3. The pulse rate of a population of 20 volunteers is tested before exercise; and the pulse rate of another 20 volunteers is tested 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

No

4. The US Mint selects ten pennies from the production line to test the hypothesis that the mean weight of each penny is at most 4 grams. The normally-distributed weights (in grams) of these pennies are as follows: 4, 10, 10, 5, 4, 10, 6, 4, 9, 6. Assume = 0.10.

· 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 3.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 5, 6, 5, 1, 7, 4, 1, 1, 1, 2, 2, 9, 8, and 10 grams. Assume = 0.05.

· 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 501 consumers two choices: Do they prefer Coke or Pepsi? Exactly 316 of those surveyed state that they prefer Coke. Assuming that = 0.10, test the hypothesis that the proportion of the population that prefers Coke is 50%.

· 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:

10.3 12.3 13.5 10.4 11.6 10.9 11.5 12.4 10.1 10.7

The times required by sprinters in the second group are as follows:

11.5 10.3 15.1 13.9 14.7 10.2 13.2 16.0 11.7 10.6

Assuming that = 0.02, 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?

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Independent or dependent samples, Z-test and critical value are discussed.

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