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SAT and ACT Tests Because they enable efficient procedures for evaluating answers, multiple choice questions are commonly used on standardized tests, such as the SAT or ACT. Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume that both questions have correct answers of “a.”
a. After listing the 25 different possible samples, find the proportion of correct answers in each sample, then construct a table that describes the sampling distribution of the sample proportions of correct responses.
b. Find the mean of the sampling distribution of the sample proportion.
c. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of correct responses? Does the mean of the sampling distribution of proportions always equal the population proportion?
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Chapter 6 Solutions
MyLab Statistics with Pearson eText -- Standalone Access Card -- for Essentials of Statistics
- You assume that the annual incomes for certain workers are normal with a mean of $28,500 and a standard deviation of $2,400. What’s the chance that a randomly selected employee makes more than $30,000?What’s the chance that 36 randomly selected employees make more than $30,000, on average?arrow_forwardWhat’s the chance that a fair coin comes up heads more than 60 times when you toss it 100 times?arrow_forwardSuppose that you have a normal population of quiz scores with mean 40 and standard deviation 10. Select a random sample of 40. What’s the chance that the mean of the quiz scores won’t exceed 45?Select one individual from the population. What’s the chance that his/her quiz score won’t exceed 45?arrow_forward
- Suppose that you take a sample of 100 from a population that contains 45 percent Democrats. What sample size condition do you need to check here (if any)?What’s the standard error of ^P?Compare the standard errors of ^p n=100 for ,n=1000 , n=10,000, and comment.arrow_forwardSuppose that a class’s test scores have a mean of 80 and standard deviation of 5. You choose 25 students from the class. What’s the chance that the group’s average test score is more than 82?arrow_forwardSuppose that you collect data on 10 products and check their weights. The average should be 10 ounces, but your sample mean is 9 ounces with standard deviation 2 ounces. Find the standard score.What percentile is the standard score found in part a of this question closest to?Suppose that the mean really is 10 ounces. Do you find these results unusual? Use probabilities to explain.arrow_forward
- Suppose that you want to sample expensive computer chips, but you can have only n=3 of them. Should you continue the experiment?arrow_forwardSuppose that studies claim that 40 percent of cellphone owners use their phones in the car while driving. What’s the chance that more than 425 out of a random sample of 1,000 cellphone owners say they use their phones while driving?arrow_forwardSuppose that the average length of stay in Europe for American tourists is 17 days, with standard deviation 4.5. You choose a random sample of 16 American tourists. The sample of 16 stay an average of 18.5 days or more. What’s the chance of that happening?arrow_forward
- How do you recognize that a statistical problem requires you to use the CLT? Think of one or two clues you can look for. (Assume quantitative data.)arrow_forwardSuppose that you take a sample of 100 from a skewed population with mean 50 and standard deviation 15. What sample size condition do you need to check here (if any)?What’s the shape and center of the sampling distribution for ?What’s the standard error?arrow_forwardQuestion 3 The following stem-and-leaf displays the weekly salary of employees at this firm. Stem-and-Leaf Display Leaf Unit = 10.0 N=x 5 3 00123 12 4 0125888 (y) 5 11234456777 z 6 13568 5 7 154 2 8 46 i. Determine the value of x, y and z. [3] ii. What is the value of the median? [2] iii. Find the mode of this data set. iv. Calculate the range [1] [2]arrow_forward
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