Exam 13: Testing Hypotheses About Means

When comparing two means, which situation is most likely to lead to a result that is statistically significant? (Consider all other factors equal, such as significance level and standard deviations.)

What is the estimated effect size for a test for the difference between two population means with independent samples with sizes of 25 and 35 respectively and a pooled t-test statistic of t = -2.34?

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. -This is an example of

Use the following information for questions: A pooled two independent samples t-test was conducted to compare the average number of accidents for male drivers to that for female drivers. The t-test statistic was 2.4 and the sample sizes were 32 males and 30 females. -Based on Cohen's interpretation, this effect is

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. -Which of the following is an appropriate conclusion?

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion?

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. -Find the p-value for testing whether the population mean response is more than 100 mph?

Use the following information for questions: A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54). -How would a 99% confidence interval compare to the 95% confidence interval?

Use the following information for questions: A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54). -Based on this interval, what is the decision for testing H₀: $\mu$ = 50 versus H_a: $\mu$$\neq$ 50 at the 10% significance level?

An experiment is conducted with 15 seniors who are taking Spanish at Oak View High School. A randomly selected group of eight students is first tested with a written test and a day later with an oral exam. To avoid order effects, the other seven students are tested in reverse order. The instructor is interested in the difference in grades between the two testing methods. SPSS is used to obtain descriptive statistics for the grades of the two tests. Is there a significant difference between the mean grades using the two different testing methods? Use $\alpha$ = 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 is the p-value?

Use the following information for questions: A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54). -Based on this interval, what is the decision for testing H₀: $\mu$ = 50 versus H_a: $\mu$$\neq$ 50 at the 5% significance level?

The average time in years to get an undergraduate degree in computer science was compared for men and women. Random samples of 100 male computer science majors and 100 female computer science majors were taken. Choose the appropriate parameter(s) for this situation.

Spatial perception is measured on a scale from 0 to 10. A group of 9^th grade students are tested for spatial perception. SPSS was used to obtain descriptive statistics of the spatial perception scores in the sample. Using $\alpha$ = 0.01, is the mean score significantly different from 5?

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 are the appropriate null and alternative hypotheses?

Use the following information for questions: A group of women suffering from various types of obsessive fear is given a therapeutic course to learn how to handle their fear. At the beginning of the course the women are given a questionnaire to determine how afraid they are. Fear scores range between 100 and 400. SPSS is used to obtain descriptive statistics. Output is shown below. The course coordinator wishes to test if the women score significantly lower than 250. -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. -Are the results statistically significant?

The primary purpose of a significance test is to

Use the following information for questions: A large car insurance company is conducting a study to see if male and female drivers have the same number of accidents, on average, or if male drivers (who tend to be thought of as more aggressive drivers) have more. Data on the number of accidents in the past 5 years is collected for randomly selected drivers who are insured by this company. An analysis of the results produced the following output. -Note that the p-value for the two-sided test is p = 0.0193. What would be the p-value for the one-sided test of interest here?

Use the following information for questions: An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2). 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 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 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 are the appropriate null and alternative hypotheses?