Practice Exam Answers

The scientist would like to know if these data provide convincing evidence that the distribution of education differs for these regions in the population of all tristate residents. Are the conditions for inference met?

Which is the correct interpretation of the standard deviation?

Which of the following histograms correctly displays the distribution?

The conditions for inference are met. What is the value of the chi-square test statistic and what are the degrees of freedom for this test?

A prior study estimated hat p as 34 percent The analysts would like to conduct a second study on the same topic with a margin of error, cap e , of 0 point 0 2 7 and a confidence level of 90 percent ( z to the th power times -score 1 point 6 4 5 ). What is the minimum sample size that should be used so the estimate of hat p will be within the required margin of error of the population proportion? n is equal to hat p times open paren 1 minus hat p close paren times open paren the fraction with numerator z to the th power times and denominator cap e close paren squared

A certain oat cereal manufacturer boasts that adults who eat its cereal every day have lower cholesterol levels. To test this claim, a nurse measures the cholesterol levels of 18 patients. These patients are instructed to eat the oat cereal every day for four weeks. At the end of this four-week period, the nurse measures the cholesterol levels again. The differences in cholesterol levels open paren before minus after close paren are listed. A negative difference means that a patient’s cholesterol level increased over the four weeks. negative 18 comma 5 comma 9 comma negative 1 comma 0 comma 4 comma 3 comma negative 2 comma 0 comma 11 comma 5 comma 12 comma negative 5 comma 1 comma negative 3 comma 4 comma 8 comma 9 Assuming the conditions for inference are met, what is the test statistic for testing the hypotheses ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is greater than 0 ?

A carnival game is designed so that approximately 10 percent of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0 point 1 0 Are the conditions for inference met for conducting a z - test for one proportion?

A shipping company claims that 95 percent of packages are delivered on time. A student wants to conduct a simulation to estimate the number of packages that would need to be randomly selected in order to find a package that was not delivered on time. What is an appropriate assignment of digits to carry out this simulation?

The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared to customers who drink coffee. Customers using their own cups get a 5 percent discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let p sub cap e s p r e s s o is equal to the true proportion of customers who drink espresso and use their own cup and p sub cap c o f f e e is equal to the true proportion of customers who drink coffee and use their own cup. Which of the following is the correct standardized test statistic and cap p - value for the hypotheses, ratio of cap h sub 0 to p sub cap e s p r e s s o minus p sub cap c o f f e e is equal to 0 and ratio of cap h sub A to p sub cap e s p r e s s o minus p sub cap c o f f e e is less than 0 ? Use the z -table.

At a large company retreat, management orders subs for lunch. They hypothesize that 50 percent of the attendees will choose a turkey sub, 40 percent will choose a ham sub, and 10 percent will choose a vegetarian sub. Before placing the order, they select a random sample of 50 attendees and determine the type of sub they prefer. The management would like to know if there is convincing evidence that the distribution of sub preference differs from 50 percent turkey, 40 percent ham, and 10 percent vegetarian. Are the conditions for inference met?

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 ratio of cap h sub 0 to mu is equal to 2 versus ratio of cap h sub A to mu is less than 2 , where mu is equal to the true mean run time for all vacuums of this model. The power of this test to reject ratio of cap h sub 0 to mu is equal to 2 when mu is equal to 1 point 7 5 is 0 point 0 8 6 5 using a significance level of 0 point 0 5 Which combination of sample size and significance level would increase the power of this test the most?

One of Natalia’s professors claims that 13 percent of the students at their college frequently wear hats. Natalia feels that the actual rate is much lower. She selects a random sample of 100 students at the college and finds that only 9 of them wear hats frequently. To determine if her data provide convincing evidence that the true proportion is less than 13 percent , she conducts 200 trials of a simulation. Natalia is testing the hypotheses: ratio of cap h sub 0 to p is equal to 13 percent and ratio of cap h sub A to p is less than 13 percent , where p is equal to the true proportion of students at the college who frequently wear hats. Based on the results of the simulation, what is an estimate of the cap p - value of the test? Expand Image

What is the z to the th power times critical value for constructing a 95 percent confidence interval for a proportion? Use the z -table.

In a large high school, 37 percent of the teachers believe that five minutes is not enough time for students to change classes. However, 89 percent of the students believe that five minutes is not enough time for students to change classes. Let hat p sub cap f and hat p sub cap s be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the mean of the sampling distribution of hat p sub cap f minus hat p sub cap s ?

A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65 percent of households supported starting school earlier. They ask a random sample of 100 households this year, and 70 percent state they would support starting the school year earlier. The cap p -value for the test of the hypotheses, ratio of cap h sub 0 to p is equal to 0 point 6 5 and ratio of cap h sub A to p is not equal to 0 point 6 5 , is 0 point 2 9 What is the correct interpretation of this value?

A company is started by four friends. The company was Erica’s idea, so she wants to fill 70 percent of the orders. Jen, Heather, and Tonya each agree to fill 10 percent of the orders. After a successful first year, Erica wants to determine if the distribution of the number of orders filled is adhering to the agreed-upon percentages. To do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. Are the conditions for inference met?

Claire flips a coin 4 times. Using the table, what is the probability that the coin will show tails at most once? Number of Tails 0 1 2 3 4 Probability 0 point 0 6 0 point 2 5 0 point 3 8 0 point 2 5 0 point 0 6

The distribution of the number of items washed in a standard load of laundry is skewed left with a mean of 41 items and a standard deviation of 7 point 7 items. What is the probability that 50 randomly selected loads of laundry have a mean of more than 39 point 5 items?

A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90 percent confidence interval for the true mean weight of bags of grapes from this store to be open paren 15 point 8 7 5 comma 16 point 5 9 5 close paren ounces. What is the correct interpretation of the 90 percent confidence interval?

A bottled water company bottles varying sizes of water, from 8 -ounce to 1 -gallon containers. The company has determined that the mean quantity in their 20 -ounce bottles is 20 point 8 ounces with a standard deviation of 0 point 6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is recorded. Which of the following values of the mean of the sample is most likely to occur if the true mean number of ounces is 20 point 8 ?