Unit Test — Cumulative exam Answers

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 30 pairs of pants. What is the shape of the distribution of the sample mean for all possible random samples of size 30 from this population?

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. What is an appropriate assignment of digits for this simulation?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The minimum of the ages of the officers is 15. The table displays all possible samples of size 2 and the corresponding minimum for each sample.Using the minimums in the table, is the sample minimum an unbiased estimator?

A junior at a large high school wants to estimate the amount of time it takes to log in to a school computer. He randomly selects 35 students and records the amount of time it takes to log in. The junior constructs a 95% confidence interval for the true mean amount of time it takes to log in to a school computer. Which of the following would decrease the margin of error?

A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups?Find the z-table here.

A teacher would like to estimate the mean amount of time it takes for students taking this statistics class to complete this multiple-choice assessment item. To do so, she selects a random sample of 50 students enrolled in this statistics class and records the amount of time (in minutes) it takes them to complete this question. The standard error of the mean is 0.27 minutes. What is the interpretation of the standard error of the mean?

A man owns five bow ties. He chooses one bow tie at random to wear on any given day. The polka-dot bow tie is his favorite, so his random process uses a larger probability for that bow tie. The rest of the bow ties are given equal probabilities of being chosen, as shown in the table.Polka DotStripesCheckeredArgylePaisley0.40????

Animal shelters in a county need at least 15% of their animals to be adopted weekly to have room for the new animals that are brought into the various shelters. The county manager takes a random sample of shelters each week to estimate the overall proportion of animals that are adopted. If he concludes that the proportion has dropped below 15%, he will not accept any new animals into the shelters that week. He tests the hypotheses: H0: The adoption rate is 15%, and Ha: The adoption rate is less than 15%. What is a Type I error, and what is its consequence in this context?

A professional basketball player typically attempts 8 free throws per game. Let X represent the number of free throws made out of 8. The distribution for X is shown in the table.What is the expected value of the distribution?

A medical researcher claims that 60% of people with shellfish allergies do not have their first allergic reaction until adulthood. This value seems suspicious to a class of statistics students, so they ask an SRS of 30 adults with a shellfish allergy when they experienced their first allergic reaction. Fourteen of the adults experienced their first allergic reaction in adulthood. To see if this result is surprising, the class conducts a simulation to estimate the probability of obtaining a sample result as low as the one in their sample.Let 0–5 represent "adulthood” and 6–9 represent "before adulthood.”Using the line of random numbers, how many "adulthood” responses are in the first trial of the simulation?

A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, 2 hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of 5 vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. They would like to know if there is convincing evidence that the true mean run time differs from 2 hours. The consumer group plans to test the hypotheses = 2 versus < 2, where μ = the true mean run time for all vacuums of this model.

A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table.The conditions for inference are met. The 95% confidence interval for the mean difference (twin 1 – twin 2) in height is (–0.823, 0.573). What is the correct interpretation of this interval?

A racecar driver has a 0.05 probability of winning any given race in a season. There are 16 races in a season, and whether or not the driver wins one race is independent of whether he wins any other race. Let X represent the number of races the driver wins in the season.Have the conditions for a binomial setting been met for this scenario?

The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses pounds; pounds. What is a Type II error in this situation?

Can you train yourself to become better at holding your breath? An experiment was designed to find out. A group of 12 volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds):Group 1: 90, 88, 70, 110, 75, 105Group 2: 40, 48, 35, 50, 55, 62

A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. What is the appropriate inference procedure?

The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. The student would like to test H0: μ = 20 versus Ha: μ > 20, where μ = the true mean travel time for all students who attend this school. The conditions for inference are met. The test statistic is t = 2.88 and the P-value is between 0.0025 and 0.005. What conclusion should be made at the significance level, ?

Consider the given probability histogram of a binomial random variable.

The prices of houses in the US is strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 30 houses and records the mean price. What is the best description for the sampling distribution?

The owner of an apple orchard would like to estimate the mean number of usable apples produced per tree in his large orchard. He selects a random sample of 10 trees from his large orchard. This dotplot displays the number of usable apples produced for each of these trees.Are the conditions for constructing a t confidence interval met?