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1. A hospital claims that the mean wait time for emergency room patients is at least 55 minutes. A group of researchers believe that this is not accurate, and want to show that the mean wait time is less than 55 minutes. Identify the group’s null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
2. Which of the following results in the null hypothesis μ≥38 and alternative hypothesis μ<38?
3. The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the largest mean.
4. A study is planned to research the effects of drinking coffee on hours of sleep. Would an experimental or observational study design be more appropriate?
5. The answer choices below represent different hypothesis tests. Which of the choices are one-tailed tests? Select all correct answers.
6. The following frequency table summarizes a set of data. What is the five-number summary?
7. Suppose the number of dollars spent per week on groceries is normally distributed. If the population standard deviation is 7 dollars, what minimum sample size is needed to be 90% confident that the sample mean is within 3 dollars of the true population mean? Use the table above for the z-score, and be sure to round up to the nearest integer.
8. The average length of an eel from a population of short-finned eels is unknown. A random sample from the population yields a sample mean of x¯=1.9 feet. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.6 feet. Use the Empirical Rule to construct a 95% confidence interval for the true population mean length.
9. A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is not 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime. The following is the setup for this hypothesis test: H0:p = 0.35 Ha:p ≠ 0.35   Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
10. What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−1.73? (Do not round your answer; compute your answer using a value from the table below.)
11. A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 454 people have Internet access. The following is the setup for this hypothesis test: H0:p=0.63 Ha:p<0.63 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
12. Jamie, a bowler, claims that her bowling score is less than 168 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She bowls 17 games. The mean score of the sample games is 155 points. Jamie knows from experience that the standard deviation for her bowling score is 19 points. H0: μ≥168; Ha: μ<168 α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
13. An economist is studying the link between the total value of a country’s exports and that country’s gross domestic product, or GDP. The economist recorded the GDP and Export value (in millions of $’s) for 30 nations for the same fiscal year. This sample data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.
14. Elizabeth claims that her average typing speed is greater than 87 words per minute. From recent typing trials, it is observed that Elizabeth has a sample typing speed mean of 98.9 words per minute (based on 18 trials). Given the sample data below, determine whether to reject the null hypothesis, or fail to reject the null hypothesis and also come to a conclusion regarding the claim.
15. A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test?
16. A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20% of the complaints should have been filed on Monday. She randomly selected 50 complaints and checked the day that they were submitted. In those complaints 13 were submitted on a Monday.
17. A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000.
18. John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,11).
19. A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x¯=77, with a margin of error of 10.
20. The scatter plot below shows data relating elementary students’ reading scores and how many books they read over the summer. Which of the following patterns does the scatter plot show?