Concept explainers
For Exercises 2 through 12, perform each of these steps. Assume that all variables are normally or approximately
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.
12. Mistakes in a Song A random sample of six music students played a short song, and the number of mistakes in music each student made was recorded. After they practiced the song 5 times, the number of mistakes each student made was recorded. The data are shown. At α = 0.05, can it be concluded that there was a decrease in the
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- Molly works for a meat producer, and she needs to determine whether containers of ground beef have the correct fat content. She obtains a random sample of 120 containers of ground beef and finds that 84 percent have the correct fat content. Molly then conducts a hypothesis test of H0:p=0.80H0:p=0.80 versus Ha:p≠0.80Ha:p≠0.80 and calculates a test statistic of 1.10 with a pp-value of 0.273. Which of the following best represents the meaning of the pp-value? If the population proportion is 0.84, the probability of observing a sample proportion of 0.80 is 0.273. A If the population proportion is 0.84, the probability of observing a sample proportion of at least 0.04 less than 0.84 is 0.273. B If the population proportion is 0.80, the probability of observing a sample proportion within 0.04 of 0.80 is 0.273. C If the population proportion is 0.80, the probability of observing a sample proportion at least 0.04 greater than 0.80 is 0.273. D If the…arrow_forwardMolly works for a meat producer, and she needs to determine whether containers of ground beef have the correct fat content. She obtains a random sample of 120 containers of ground beef and finds that 84 percent have the correct fat content. Molly then conducts a hypothesis test of H0:p=0.80H0:p=0.80 versus Ha:p≠0.80Ha:p≠0.80 and calculates a test statistic of 1.10 with a pp-value of 0.273. Which of the following best represents the meaning of the pp-value? If the population proportion is 0.84, the probability of observing a sample proportion of 0.80 is 0.273. A If the population proportion is 0.84, the probability of observing a sample proportion of at least 0.04 less than 0.84 is 0.273. B If the population proportion is 0.80, the probability of observing a sample proportion within 0.04 of 0.80 is 0.273. C If the population proportion is 0.80, the probability of observing a sample proportion at least 0.04 greater than 0.80 is 0.273. D If the…arrow_forwardUse the traditional method in testing the hypothesis in the problems below. In each problem, state the following:a. State the hypotheses and identify the claim.b. Find the critical value(s)c. Find the test value The manager of the cosmetics section of a large department store wants to determine whether newspaper advertising really does affect sales. For her experiment, she randomly selects 15 items currently in stock and proceeds to establish a baseline. The 15 items are priced at their usual competitive values, and the quantity of each item sold for a 1-week period is recorded. Then, without changing their price, she places a large ad in the newspaper, advertising the 15 items. Again, she records the quantity sold for a 1-week period. The results follow. Item 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15No. of Items Sold Before Ad 25 18 3 42 16 20 23 32 60 40 27 7 13 23 16No. of Items Sold After Ad 32 24 7 40 19 25 23 35 60 43 28 11 12 32 28arrow_forward
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- Suppose that you are to conduct the following hypothesis test: ?0:?1:??=≠450450H0:μ=450H1:μ≠450 Assume that you know that ?=105σ=105, ?=50n=50, ?¯=430.05x¯=430.05, and take ?=0.005α=0.005. Draw the sampling distribution, and use it to determine each of the following: A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,?)(−∞,a) is expressed (-infty, a), an answer of the form (?,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,?)∪(?,∞)(−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic:arrow_forwardSuppose that you are to conduct the following hypothesis test: ?0:?1:??=≠450450H0:μ=450H1:μ≠450 Assume that you know that ?=105σ=105, ?=50n=50, ?¯=430.05x¯=430.05, and take ?=0.005α=0.005. Draw the sampling distribution, and use it to determine each of the following: A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,?)(−∞,a) is expressed (-infty, a), an answer of the form (?,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,?)∪(?,∞)(−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic: C. The p-value isarrow_forwardIf all other values are held constant, what happens to the value of t when sample size increases ?arrow_forward
- In quality–control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H0: The production process is performing satisfactorily and Ha: The process is performing in an unsatisfactory manner. Accordingly, α is sometimes referred to as the producer's risk, while β is called the consumer's risk. An injection molder produces plastic golf tees with a mean weight of 0.252 ounce. To investigate whether the injection molder is operating satisfactorily, 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the accompanying table. Complete parts a through g. 0.248 0.251 0.249 0.250 0.255 0.251 0.251 0.248 0.248 0.251 0.254 0.252 0.256 0.251 0.252 0.253 0.250 0.254 0.254 0.254 0.251 0.251 0.252 0.249 0.249 0.251 0.252 0.253 0.248 0.252 0.252 0.252 0.249 0.252 0.249 0.253 0.252 0.249 0.249 0.251 b.…arrow_forwardIn quality–control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H0: The production process is performing satisfactorily and Ha: The process is performing in an unsatisfactory manner. Accordingly, α is sometimes referred to as the producer's risk, while β is called the consumer's risk. An injection molder produces plastic golf tees with a mean weight of 0.252 ounce. To investigate whether the injection molder is operating satisfactorily, 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the accompanying table a. Write H0 and Ha in terms of the true mean weight of the golf tees, μ. A. H0: μ=0.252 Ha: μ<0.252 B. H0: μ=0.252 Ha: μ≠0.252 C. H0: μ=0.252 Ha: μ>0.252 D. H0: μ≠0.252 Ha: μ=arrow_forwardThe level of significance for a hypothesis is 0.01. If you compute a p-value of 0.0157 what decision should you make?arrow_forward
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