Exam 13: Testing Hypotheses About Means

Use the following information for questions: An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. -What is the value of the test statistic?

Each of the following presents a two-sided confidence interval and the alternative hypothesis of a corresponding hypothesis test. In which case can we not use the given confidence interval to make a decision at a significance level $\alpha$ = .05?

Use the following information for questions: An instructor wanted to prove that writing with the non-dominant hand takes longer on average than writing with the dominant hand. A significance level of 5% will be used. Ten students randomly sampled from a large class each wrote the word "Statistics" twice; once with their dominant hand and once with their non-dominant hand, in random order. The average time to write using their dominant hands was 5 seconds, while the average time to write with their non-dominant hand was 10 seconds. The standard deviation of the difference was 7.9 seconds, and the standard error was 2.498. Assume that writing times with each hand are normally distributed. -What is the value of the t-test statistic?

Use the following information for questions: A bank official wants to assess if the average delays for two airlines are different.Let $µ_1$ = average delay for Airline 1 and $µ_2$ = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 6 minutes delay with a standard deviation of 5 minutes. A random sample of 10 flights for Airline 2 shows an average of 12 minutes delay with a standard deviation of 5 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom. -What is the value of the test statistic?

Use the following information for questions: A researcher wants to assess if there is a difference in the average life spans between men and women in Japan. Let $µ_1$ = average life span of Japanese women and $µ_2$ = average life span of Japanese men. A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years. A random sample of 10 men showed an average lifespan of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed and that the population variances are equal. -Which of the following is an appropriate conclusion?

Use the following information for questions: In the survey of a random sample of students at a university, two questions were "How many hours per week do you usually study?" and "Have you smoked marijuana in the past six months?" An analysis of the results produced the following Minitab output: -Based on the information given in the output, what conclusion can be made about the difference in time spent studying for the two groups?

If the word significant is used to describe a result in a news article reporting on a study,

Use the following information for questions: An instructor wanted to prove that writing with the non-dominant hand takes longer on average than writing with the dominant hand. A significance level of 5% will be used. Ten students randomly sampled from a large class each wrote the word "Statistics" twice; once with their dominant hand and once with their non-dominant hand, in random order. The average time to write using their dominant hands was 5 seconds, while the average time to write with their non-dominant hand was 10 seconds. The standard deviation of the difference was 7.9 seconds, and the standard error was 2.498. Assume that writing times with each hand are normally distributed. -What is the value of the t-test statistic?

Use the following information for questions: A counselor wants to show that for men who are married by the time they are 30, $\mu$ = average age when the men are married is not 21 years old. A random sample of 10 men who were married by age 30 showed an average age at marriage of 22.2, with a sample standard deviation of 1.9 years. Assume that the age at which this population of men get married for the first time is normally distributed. -Which of the following is an appropriate conclusion?

Researchers want to see if men have a higher blood pressure than women do. A study is planned in which the blood pressures of 50 men and 50 women will be measured. What's the most appropriate alternative hypothesis about the means of the men and women?

Use the following information for questions: It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resultingt-statistic was 1.80. -Assuming the conditions are met, based on the t-statistic of 1.80 the appropriate decision for this test using $\alpha$ = 0.05 is:

Explain what the effect size measures.

According to the CIRP Freshman Survey, UCLA's annual survey of the nation's entering students at four-year colleges and universities, conducted in 2010, female students were far less likely to report high levels of emotional health than male students. The difference was reported as statistically significant. Choose the appropriate parameter(s) for this situation.

Use the following information for questions: A safety officer wants to prove that $\mu$ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed. -What is the p-value?

Use the following information for questions: A sample of n = 9 men are asked. "What's the fastest you've ever driven a car?"The sample mean is 120 mph and the standard deviation is 30. -Give an appropriate conclusion using a 1% level of significance.

Use the following information for questions: A counselor wants to show that for men who are married by the time they are 30, $\mu$ = average age when the men are married is not 21 years old. A random sample of 10 men who were married by age 30 showed an average age at marriage of 22.2, with a sample standard deviation of 1.9 years. Assume that the age at which this population of men get married for the first time is normally distributed. -What is the p-value?

In each of the following cases, we wish to test the null hypothesis H₀: $\mu$ =18. In which case can this null hypothesis be rejected at a significance level $\alpha$ = 0.05?

Use the following information for questions: A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let $µ_1$ = average age of onset for women and $µ_2$ = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal, and use the conservative "by hand" estimate for the degrees of freedom. -What are the appropriate null and alternative hypotheses?

A sociologist has been studying college instructors and is especially interested in those instructors who teach night classes. Amongst others, he collected data on the course grade from the student evaluations and the highest level of education the instructor has completed (Master or Ph.D.). If the sociologist wishes to determine how much higher the course grades are for courses taught by an instructor with a Ph.D. than those taught by an instructor with a master's degree, which inference procedure should he use?

The maximum distance at which a highway sign can be read is determined for a sample of young people and a sample of older people. The mean distance is computed for each age group. What's the most appropriate null hypothesis about the means of the two groups?