Homework

A student at a four-year college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the 35 two–year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191.

Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

Using the data from Lap 1 only, conduct a hypothesis test to determine if the mean time for completing a lap in races is the same as it is in practices.

Repeat the test in Exercise 10.83, but this time combine the data from Laps 1 and 5.

If the level of significance is 0.05, the conclusion is:

1. There is sufficient evidence to conclude that the W Division teams score fewer goals, on average, than the E teams
2. There is insufficient evidence to conclude that the W Division teams score more goals, on average, than the E teams.
3. There is insufficient evidence to conclude that the W teams score fewer goals, on average, than the E teams score.
4. Unable to determine

Elijah wants to know whether textbook costs are different for different courses of study. He selects a random sample of 33 sociology textbooks offered on a popular online site. The mean price of his sample is $74.64 with a standard deviation of $49.36. He then selects a random sample of 33 math and science textbooks from the same site. The mean price of this sample is $111.56 with a standard deviation of $66.90. Is the mean price of a sociology textbook lower than the mean price of a math or science textbook? Test at a 1% significance level.

Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. They take random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91, respectively. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The “day” subscript refers to the statistics day students. The “night” subscript refers to the statistics night students. An appropriate alternative hypothesis for the hypothesis test is:

1. μ_day > μ_night
2. μ_day < μ_night
3. μ_day = μ_night
4. μ_day ≠ μ_night

Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls.

Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a standard deviation of seven mpg. Thirty-one non-hybrid sedans get a mean of 22 mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test to evaluate the manufacturers claim.

One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement “I’m pleased with the way we divide the responsibilities for childcare.” The ratings went from one (strongly agree) to five (strongly disagree). Table 10.29 contains ten of the paired responses for husbands and wives. Conduct a hypothesis test to see if the mean difference in the husband’s versus the wife’s satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife).

We are interested in whether the proportions of conferred physical science degrees for people aged 21 to 24 are the same for White and Black people in the United States. The number of conferred degrees for White people in a given year is 4,930. Five hundred eighty were aged 21 to 24. The estimate for Black people is 330. Forty were aged 21 to 24. We will let people with conferred physical science degrees be our population.

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

An appropriate null hypothesis is:

1. $p2022 \le p2021$
2. $p2022 \ge p2021$
3. $\mu 2022 \le \mu 2021$
4. $p2022 > p2021$

Researchers conducted a study to find out if there is a difference in the use of eReaders by different age groups. Randomly selected participants were divided into two age groups. In the 16- to 29-year-old group, 7% of the 628 surveyed use eReaders, while 11% of the 2,309 participants 30 years old and older use eReaders.

Two computer users were discussing tablet computers. A higher proportion of people ages 16 to 29 use tablets than the proportion of people age 30 and older. Table 10.31 details the number of tablet owners for each age group. Test at the 1% level of significance.

While her husband spent 2½ hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of 67 men, 24 said they enjoyed the activity. Eight of the 24 women surveyed claimed to enjoy the activity. Interpret the results of the survey.

Joan Nguyen recently claimed that the proportion of college-age men with at least one pierced ear is as high as the proportion of college-age women. She conducted a survey in her classes. Out of 107 men, 20 had at least one pierced ear. Out of 92 women, 47 had at least one pierced ear. Do you believe that the proportion of men has reached the proportion of women?

"To Breakfast or Not to Breakfast?" by Richard Ayore

In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the 18th, 20th, …, birthdays. During this time, one looks back to see what they have achieved for the past year and also focuses ahead for more to come.

If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine.

Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, “This is why I always work more hours than you guys!”

And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in Table 10.32, solve our problem.

Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. The data are recorded in Table 10.33. Do you think that their cholesterol levels were significantly lowered?

If the p-value is 0.0062 what is the conclusion (use α = 0.05)?

1. The method has no effect.
2. There is sufficient evidence to conclude that the method reduces the proportion of patients who develop heart disease after four years.
3. There is sufficient evidence to conclude that the method increases the proportion of patients who develop heart disease after four years.
4. There is insufficient evidence to conclude that the method reduces the proportion of patients who develop heart disease after four years.

If α = 0.05, the p-value and the conclusion are

1. 0.0014; There is sufficient evidence to conclude that the blood pressure decreased after the training.
2. 0.0014; There is sufficient evidence to conclude that the blood pressure increased after the training.
3. 0.0155; There is sufficient evidence to conclude that the blood pressure decreased after the training.
4. 0.0155; There is sufficient evidence to conclude that the blood pressure increased after the training.

A local cancer support group believes that the estimate for new female breast cancer cases in the south is higher in Year 2 than in Year 1. The group compared the estimates of new female breast cancer cases by southern state in Year 1 and in Year 2. The results are in Table 10.35.

A politician asked their staff to determine whether the underemployment rate in the northeast decreased year over year. The results are in Table 10.37.