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It is believed that $70\%$of males pass their drivers test in the first attempt, while $65\%$of females pass the test in the first attempt. Of interest is whether the proportions are in fact equal.

Indicate if the hypothesis test is for :

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a

relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference

between their jumping and relaxed times would be zero. Test their hypothesis.

A new medicine is said to help improve sleep. Eight subjects are picked at random and given the medicine. The means

hours slept for each person were recorded before starting the medication and after.

100. We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same for the whites and the blacks races in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for white females is 4,930 . Five hundred eighty were aged 15 to 24 . The estimate for black females is 330 . Forty were aged 15 to 24 . We will let female suicide victims be our population.

101. Elizabeth Mjelde, an art history professor, was interested in whether the value from the Golden Ratio formula, $\left(\frac{\text{larger + smaller dimension}}{\text{larger dimension}}\right)$was the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920 to 1942 . Thirty-seven early works were sampled, averaging $1.74$ with a standard deviation of $0.11$. Sixty-five of the later works were sampled, averaging $1.746$ with a standard deviation of $0.1064$. Do you think that there is a significant difference in the Golden Ratio calculation?

A study was conducted to investigate how effective a new diet was in lowering cholesterol. Results for the

randomly selected subjects are shown in the table. The differences have a normal distribution. Are the subjects’

cholesterol levels lower on average after the diet? Test at the $5\%$level.

A new prep class was designed to improve SAT test scores. Five students were selected at random. Their scores on two practice exams were recorded, one before the class and one after. The data recorded in the table given below. Are the scores, on average, higher after the class? Test at a $5\%$level.

102. A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different?

A study is done to determine if Company A retains its workers longer than Company B. Company A samples $15$workers, and their average time with the company is five years with a standard deviation of $1.2.$Company B samples $20$workers, and their average time with the company is $4.5\text{years}$with a standard deviation of $0.8.$The populations are normally distributed.

a. Are the population standard deviations known?

b. Conduct an appropriate hypothesis test. At the $5\%$significance level, what is your conclusion?

• "2011" subscript: 2011 group.
• "2010" subscript: 2010 group

(a) a test of two proportions
(b) a test of two independent means
(c) a test of a single mean
(d) a test of matched pairs.