An extensive study in Antarctica concluded that the mean height of adult emperor penguins in the wild is 44.5 in. Cassandra believes that captive emperor penguins have a greater mean height due to better nutrition. To test this idea, she decides to conduct a one-sample t-test to see if the mean height of captive emperor penguins is greater than 44.5 in. She selects a simple random sample of 26 penguins from different zoos around the country and has each penguin measured. The summary statistics of the sample are given below. Sample size Sample mean n = 26 x = 45.6 in Sample standard deviation s = 4.3 in The heights of emperor penguins are normally distributed, and there are no outliers in the sample. Construct the null and alternative hypothesis for the appropriate one-sample t-test for the mean height of captive emperor penguins. H₁: = Ho:

A researcher hypothesizes that different colors of cars result in different average speeds.  To test this claim, she took a random sample of 20 people who own 4 different colors of colors of cars  (n = 20, N = 80, G = 4), and she then tracks their average speed on the highway for a week of driving.  The following ANOVA table has some of her results.  Please help her answer her research questions by completing the following ANOVA table below and answering the follow-up questions.  Be sure to label your answers with the appropriate letter and show all your work! Source  Sums of Squares     df   Mean Square        F     Effect (between)             Error (within) 100.90     ------ Total 170.10     ------- ------ a) What is the Sums of Squares (SS) between (effect)? b) What are the Mean Square (MS) between (effect) and the MS within (error)? c) What are the degrees of freedom (df) between, the df within, and the df total? d) What is the overall F-statistic? e) Based on the…

A successful basketball player has a height of 6 feet 11 ​inches, or 211 cm. Based on statistics from a data​ set, his height converts to the z score of 5.17. How many standard deviations is his height above the​ mean?

The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings (Coca-Cola Company website, February 3, 2009). Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Cola's corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard deviation of s=101.9. Answer questions 8-10.

An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 240 Fundash runners and 200 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 240 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.2 minutes. The 200 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.4 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ1 , of Fundash is not equal to the mean completion time, μ2 , of Coolsprint?…

Two social scientists wanted to know if more violent crimes are committed when the temperature goes up. They measured the high temperature for each day during the year in Atlanta and compared the temperature for that day to the Police Department’s report for the number of violent crimes for that day. What statistical test should they use to analyze the data? a. Paired t-test b. Correlation c. One Way ANOVA d. Independent Samples t-test e. Chi Square Test of Independence

The University of Georgia has several football players participating in the NFL draft this season. A few former coaches are helping the players prepare for the NFL tryout by tracking their practice performance. One coach calculates the athlete's speed in feet per second each round and then finds the mean and standard deviation for all rounds. Since the workout tested at the NFL tryout is the 40 yard dash, the coach decides to convert these speeds to yards per second instead of feet per second, where 1 yard is equal to 3 feet. Which of the following best describes what would happen to the summary statistics for the athletes? (A) The mean would increase, but the standard deviation would remain the same. (B) Both the mean and standard deviation would remain the same. (C) Both the mean and standard deviation would decrease. (D) The mean would decrease, but the standard deviation would remain the same. (E) The mean would decrease, but the standard deviation would increase.

A researcher wanted to find the best viewing distance for watching a TV screen. He recruited the following number of participants and asked them to evaluate their satisfaction of the viewing distance. Then, he conducted an ANOVA to see if there is any significant mean differences. Here are the number of participants by each group: Group 1 (4 feet) - 5 people Group 2 (7 feet) - 5 people Group 3 (10 feet) - 6 people Group 4 (13 feet) - 5 people Group 5 (16 feet) - 4 people Given the numbers as presented above, what is the degrees of freedom for within groups for this analysis? a. 4 b. 20 O c. 21 d. 25

There are many ways to measure the reading ability of children. One frequently used test is the DRP or Degree of Reading Power. The national average score in DRP test is 32. We want to determine if there is sufficient evidence at the 5% level to suggest that the mean score of all third graders in YOUR district is higher than the national mean. The DRP scores for a simple random sample of 41 third graders in that suburban school in YOUR district yielded a mean of 35.2. Assume that the population of DRP scores of third graders in that suburban school district are normally distributed with a population std.dev of 11.

A statistician changes her level of significance from .001 to .05.  What impact will this change have on her risk of making a Type I and Type II error?  Is the change in the level of significance a good decision?  Why or why not?