# EBook Problems Hypothesis S Mean

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## EBook Problems Set - Testing a Claim about a Mean: Small Samples

### Problem 1

To test the claim that the average home in a certain town is within 5.5 miles of the nearest fire station, and insurance company measured the distances from 25 randomly selected homes to the nearest fire station and found x-bar = 5.8 miles and sd = 2.4 miles. Determine what the insurance company found out with a test of significance. Check all that apply.

• Choose at least one answer.
(a) There is no evidence in the data to conclude that the distance is different from 5.5.
(b) The average of 5.8 miles observed is by chance.
(c) We cannot reject the null.
(d) There is evidence in the data to conclude that the distance is 5.5.

### Problem 2

For mothers who are between 20 and 40 years old and who gain between 20 and 35 during the course of their pregnancies, the average birth weight of their babies is 7.0 pounds and the standard deviation is 0.85 pounds. Researchers want to determine if mothers who are also between 20 and 40 years old but who gained less than 20 pounds during the course of their pregnancies will have babies that have different birth weights.

The average weight of babies born to a random sample of 64 mothers who had gained between 10-18 pounds during the course of their pregnancy was 6.83 pounds. Should we accept or fail to reject the null hypothesis and why?

(a) We reject the alternative hypothesis ( P = 0.0548) and conclude that the average weight on the infants born to mothers who gained 10-18 pounds is not different than mothers who gained 20-35 pounds.
(b) We reject the alternative hypothesis ( P = 0.1096) and conclude that the average weight on the infants born to mothers who gained 10-18 pounds is not different than mothers who gained 20-35 pounds.
(c) We fail to reject the null hypothesis and we are 94.52% that the average weight on the infants born to mothers who gained 10-18 pounds is not different than mothers who gained 20-35 pounds.
(d) We fail to reject the alternative hypothesis ( P = 0.1096) and conclude that the average weight on the infants born to mothers who gained 10-18 pounds is not different than mothers who gained 20-35 pounds.

### Problem 3

The average length of time required to complete a certain aptitude test is claimed to be 80 minutes. A random sample of 25 students yielded an average of 86.5 minutes and a standard deviation of 15.4 minutes. If we assume normality of the population distribution, is there evidence to reject the claim?

• Choose at least one answer.
(a) Yes, because the observed 86.5 did not happen by chance
(b) Yes, because the t-test statistic is 2.11
(c) Yes, because the observed 86.5 happened by chance
(d) No, because the probability that the null is true is > 0.05