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Exam 10: Introduction to Hypothesis Testing

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Question 51

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The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years. What is the p -value associated with the test statistic?

A) 0.9582
B) 1.7300
C) 0.0418
D) 0.0836

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Question 52

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If we do not reject the null hypothesis, we conclude that there ____________________(is\is not)enough statistical evidence to infer that the alternative hypothesis is true.

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Question 53

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LSAT Scores The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300. An accepted standard deviation for LSAT scores is 125. A random sample of 25 scores had an average of 1,375. {LSAT Scores Narrative} Calculate the p -value.

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:

The power of a test is measured by its capability of:

In testing the hypotheses H ₀: m = 50 vs. H ₁: m ¹ 50, the following information is known: n = 64, = 53.5, and s = 10. The standardized test statistic z equals:

Toaster Oven An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W. A consumer group suspects the actual average is more than 250 W. They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W. {Toaster Oven Narrative} Calculate the p -value of the test.

If a researcher rejects a true null hypothesis, she has made a(n)____________________ error.

You cannot commit a(n)____________________ error when the null hypothesis is true.

Increasing the probability of a Type I error will increase the probability of a Type II error.

Explain why a Type I error and a Type II error have an inverse relationship.

A random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75. Does this statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?

The probability of a Type II error is denoted by ____________________.

Suppose that 9 observations are drawn from a normal population whose standard deviation is 2. The observations are: 15, 9, 13, 11, 8, 12, 11, 7, and 10. At 95% confidence, you want to determine whether the mean of the population from which this sample was taken is significantly different from 10. a. State the null and alternative hypotheses. b. Compute the value of the test statistic. c. Compute the p -value. d. Interpret the results.

Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following a -values do we also reject the null hypothesis?

Suppose a pickup and delivery company states that their packages arrive within two days or less on average. You want to find out whether the actual average delivery time is longer than this. You conduct a hypothesis test. a. Set up the null and alternative hypotheses. b. Suppose you conclude wrongly that the company's statement about average delivery time is within two days. What type of error is being committed and what is the impact of that error? c. Suppose you conclude wrongly that the delivery company's average time to delivery is in fact longer than two days. What type of error did you commit and what is the impact of this error? d. Which error is worse from the company's standpoint, a Type I or a Type II error? Why? e. Which error is worse from a consumer standpoint, a Type I or a Type II error? Why?

To calculate the probability of a(n)____________________ error you need to specify a value of m other than the one given in the null hypothesis.

In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.

The statement of the null hypothesis always includes an equals sign (=).

For each of the following pairs of null and alternative hypotheses, determine whether or not they are statistically correct to conduct a hypothesis test. a. H ₀: m = 25, H ₁: m 25 b. H ₀: m = 30, H ₁: m > 30 c. H ₀: = 35, H ₁: > 35 d. H ₀: = 40, H ₁: 40 e. H ₀: m ¹ 60, H ₁: m = 60