Exam 13: Testing Hypotheses About Means

Use the following information for questions: Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 148 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. Is this enough evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students? -What is the value of the test statistic for testing these hypotheses using a pooled two sample t-test?

A test of H₀: $\mu$ = 0 versus H_a: $\mu$ > 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of $\alpha$ = 0.05. Which of the following will be the same for both researchers?

Use the following information for questions: Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 148 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. Is this enough evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students? -Are the results significant using a significance level of 5%?

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. -For a significance level of $\alpha$ = 0.05, are the results statistically significant?

Use the following information for questions: A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a longer mean nose length than women. -Which of the following is the correct way to state the null hypothesis?

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. -Since the sample standard deviations are fairly similar, the pooled t-test will be used (and thus the results can be found in the Equal variances assumed row of output). What is the value of the pooled t-test statistic?

Compute the effect size in a paired t-test for the mean difference based on 100 paired observations and a test statistic of t = −3.0.

The WISC scores of a sample of n = 20 5^th graders resulted in a mean of 104 with a standard deviation of 9. Is the mean score significantly higher than 100 when $\alpha$ = 0.05?

A biologist wants to measure the effect of a fertilizer on the growth of roses. She plants 20 roses in 10 plots of land with 2 roses in each plot. She randomly applies the fertilizer to one of the two roses in each plot, and then compares the average height of the roses with fertilizer to the average height of roses without fertilizer after 1 month. What is the appropriate statistical procedure she should use?

Explain the difference between the null and alternative hypotheses in hypothesis testing. Give an example.

The head circumference is measured for 25 girls and their younger twin sisters. The mean of the older twin girls was 50.23 cm and the mean of the younger twins was 49.96 cm. The standard deviation of the differences was 1 cm. Is this difference significant at a significance level of 5%?

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. -Which of the following is an appropriate conclusion?

A result is called statistically significant whenever

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. -Which of the following is an appropriate conclusion?

In a statistical test, define the events: A = the null hypothesis is true and B = the null hypothesis is rejected. Using that notation and notation on conditional probability from Chapter 7, the power of a test can be written as:

A study will be conducted to compare the proportion of earth-quake insured residents between two counties. Surveys will be mailed to a sample of residents in each county. The results will be used to assess if the county that is closer to a major earthquake fault has a higher proportion of residents with such insurance. 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: 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 test statistic for the pooled two sample t-test?

Use the following information for questions: A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a longer mean nose length than women. -A statistical test is performed for assessing if men have a longer mean nose length than women. The p-value is 0.225. Which of the following is the most appropriate way to state the conclusion?

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). -What was the mean number of loaves sold daily for the sample of 50 days?

When the alternative hypothesis is true, which one of these statements about the power of a significance test is correct?