Chapters 22-24 Flashcards
Last year the mean cost M for a one bedroom rental in a certain city was $1,200 per month. Eli is looking for a one bedroom apartment and is investigating whether the mean cost is less now than it what is was last year. A random sample of apartments had a sample mean X of of $1,180 per month. Assuming all conditions for inference are met, Eli will conduct a hypothesis test as part of his investigation. Which of the following is the correct set of hypotheses?
H0: M=1,200
Ha: M < 1,200
Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected an analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the box plot of the sample of Brand A shoe prices shoes two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means. Is the sampling distribution of the difference in sample means approximately normal?
Yes, because the size of each sample is at least 30
A sport equipment researcher investigates how different types of wood used to make baseball bats might affect batting. The researcher selected a sample of 80 batter from the summer baseball leagues and randomly assigned the batters to one of two groups: the ash bat group or the maple bat group. The mean number of hits for each group was recorded at the end of the season, and the difference in the sample means was calculated. Which of the following is the appropriate inference procedure for analyzing the results of the investigation?
A two sample T interval for a difference between population means. There were two independent groups in the experiment and data was collected in a single quantitative variable.
A sociologist will conduct a two sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor’s degrees and people with masters degrees. From a random sample of 32 people with a bachelors degree, the average salary was $55,000 with a standard deviation $3,500. From a random sample of 28 people with a masters degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic the appropriate test to investigate whether there is a difference in population means (masters degree minus bachelors degree)?
t= (58,000-55,000)/ sqrt 40,000 ^2/ 28 + 3,000^2/ 32
the denominator is the standard error of the difference in sample means or..
A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a higher price in the fall than in the spring. The reporter selected independent random samples of grocery store beef prices in November and April and compiled the mean and standard deviation for the samples. Which of the following are the correct null and alternative hypotheses for the reporters investigation, where MF represents the mean price of beef in the fall and MS represents the mean price of beef in the spring?
H0: MF-MS= 0
Ha: MF-MS > 0
The null hypothesis states that there is no difference between the population mean price of beef in the fall and the population price of beef in the spring, and the alternative hypothesis states that the population mean prive of beef is greater in the fall than in the spring.
A two sample T test for a difference in means was ‘ conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t= 1.083 and a p-value of 0.15 Based on the p-value and a significance level of alpha (0.05), which of the following is the correct conclusion?
Fail to reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench press more weight, on average, than offensive players.
The local ranger station tracked and tagged 2,844 adult female black bears in a national park. A random sample of 9 adult female black bears from those tagged had an average body weight of 203 pound with a standard deviation of 25 pounds. Which of the following is a point estimate for the population mean weight of all female black bears that are tagged?
203
For a certain brand of canned corn, the company claims that the mean weight of the contents of the can is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and a standard deviation of 0.12 ounce. A hypothesis test will be conducted to investigate whether there is evidence to support the belief that the mean is less than 15.25 ounces. Which of the following is the correct test statistic for the hypothesis test?
t = 15.18- 15.25/ (0.12/6)
The numerator of the test statistics if the sample mean (15.18) minus the assumed population mean (15.25) The denominator of the test statistic is the sample standard deviation (0.12) divided by the square root of the sample size 36 -> 6
A research scientist is conducting an experiment to determine whether a new chemical process creates a less toxic byproduct compared to the current chemical process. The scientist took a random sample of products made with the current chemical process and calculated the sample mean amount of toxic byproduct created. The scientist then took a random sample of products made with the new chemical process and calculated the sample mean amount of toxic byproduct created. The difference in the sample means (current minus new) was 2.31 liters of toxic byproduct. A hypothesis test was conducted using the following hypotheses.
H0: M current - M new = 0
Ha: M current - M new > 0
Assuming the conditions for inference were met, the scientist calculated the p-value of the test to be 0.072. Which of the following statements is the best interpretation of the P-value?
If the null hypothesis is true, the probability of observing a difference in means of at least 2.31 liters of toxic byproducts is 0.072.
A random sample of 10 employees of a company was selected to estimate the mean one way commute time for all employees at the company. The mean and standard deviation of the sample were 38 minutes and 6 minutes, respectively. Assuming all conditions for inference are met, which of the following is the margin of error, in minutes, for a 95 percent confidence interval for the population mean one way commute time?
2.262 (6/ sqrt 10)
The standard error is the sample standard deviation divided by the square root of the sample size or 6/ sqrt 10. With a sample size of 10, the number of degrees of freedom is equal to 9, and the correct critical value is t* = 2.262.
