Exam 13: Testing Hypotheses About Means

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. -Which of the following is an appropriate conclusion?

Use the following information for questions: Spatial perception is measured on a scale from 0 to 10. Two groups of 8^th grade children are tested for spatial perception. The students in group 1 were first given a short course on spatial concepts. The students in group 2 received no such instruction. SPSS was used to calculate descriptive statistics for the two samples. -What is the value of the pooled standard error?

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. -Find the p-value for testing whether using the non-dominant hand takes longer on average than using the dominant hand?

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. -What is the value of the test statistic?

A random sample of 25 third graders scored an average of 3.4 on a standardized reading test. The standard deviation was 0.95. A test is conducted to determine if the mean score is significantly higher than 3. What is the effect size of this test?

Use the following information for questions: For the variable "Time spent watching TV in Typical Day," here are results of a two-sample t-procedure that compares a random sample of men and women at a college. -Which of the following is the correct conclusion about these results using a 5% significance level?

Use the following information for questions: Spatial perception is measured on a scale from 0 to 10. Two groups of 8^th grade children are tested for spatial perception. The students in group 1 were first given a short course on spatial concepts. The students in group 2 received no such instruction. SPSS was used to calculate descriptive statistics for the two samples. -What do we know about the p-value if we wish to test if participation in the course results in significantly higher spatial perception scores?

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. -What would be the appropriate conclusion using a 5% significance level?

Use the following information for questions: A sample of passengers flying on small planes gave a mean total weight (passenger weight including shoes, clothes, and carry-on) of 200 pounds and a standard deviation of 60 pounds. -Based on Cohen's interpretation, this effect is

A company is interested in estimating the mean number of days of sick leave taken by all its employees. The firm's statistician selects a random sample of personnel files, notes the number of sick days taken by each employee over previous year. Identify the appropriate parameter for this situation and name an appropriate technique that might be performed provided the underlying assumptions are met.

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. -What is the estimated effect size for this study?

Which statement is not true about hypothesis tests?

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 true about the conditions necessary to carry out the t-test in this situation?

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. -What are the appropriate null and alternative hypotheses?

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. -Which of the following is an appropriate conclusion?

Use the following information for questions: A researcher wants to assess if the average age when women first marry has increased from 1960 to 1990. Let $µ_1$ = average age of first marriage for women in 1990 and $µ_2$ = average age of first marriage for women in 1960. A random sample of 10 women married in 1990 showed an average age at marriage of 24.95 years, with a sample standard deviation of 2 years. A random sample of 20 women married in 1960 showed an average age at marriage of 23.1 years, with a sample standard deviation of 1.5 years. Assume that age of first marriage for women is normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom. -For a significance level of $\alpha$ = 0.05, are the results statistically significant?

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 are the appropriate null and alternative hypotheses?

A random sample of 25 third graders scored an average of 3.3 on a standardized spelling test. The standard deviation was 1.06. Is the mean score significantly higher than 3?

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 do we know about the p-value for this test?

Use the following information for questions: Unoccupied seats on flights cause airlines to lose revenue. A large airline wanted to estimate its average number of unoccupied seats per flight. Based on a random sample of flights, the 95% confidence interval for mean number of unoccupied seats per flight was given as: (7.5, 9.5). -What would be the decision for testing H₀: $\mu$ = 9 versus H_a: $\mu$$\neq$ 9 at the 1% significance level?