Math 227 / Fall 2014 Instructor: David Soto Name______________________________________________ Chapter 8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ) for the indicated parameter. 1) An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten 1) thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. A) H0 : p > 0.0016 B) H0 : p = 0.0016 C) H0 : p = 0.0016 D) H0 : p < 0.0016 H1 : p 0.0016 H1 : p < 0.0016 H1 : p > 0.0016 H1 : p 0.0016 2) Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per gallon in the city. Use µ, the true average mileage of the Libra. A) H0 : µ > 23 B) H0 : µ = 23 C) H0 : µ = 23 H1 : µ 23 H1 : µ < 23 H1 : µ > 23 D) H0 : µ < 23 H1 : µ 23 3) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. A) H0 : µ = 14 B) H0 : µ = 14 C) H0 : µ < 14 D) H0 : µ > 14 H1 : µ > 14 H1 : µ < 14 H1 : µ 14 2) 3) H1 : µ 14 Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. 4) = 0.05 for a two-tailed test. 4) A) ±1.96 B) ±2.575 C) ±1.645 D) ±1.764 ^ Find the value of the test statistic z using z = p-p . pq n 5) The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 696 drowning deaths of children with 30% of them attributable to beaches. A) 2.88 B) -2.88 C) -3.05 D) 3.05 1 5) Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). 6) The test statistic in a right-tailed test is z = 0.52. 6) A) 0.0195; reject the null hypothesis B) 0.6030; fail to reject the null hypothesis C) 0.3015; fail to reject the null hypothesis D) 0.3015; reject the null hypothesis 7) The test statistic in a two-tailed test is z = 1.95. A) 0.0256; reject the null hypothesis C) 0.9744; fail to reject the null hypothesis 7) B) 0.0512; fail to reject the null hypothesis D) 0.0512; reject the null hypothesis Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. 8) An entomologist writes an article in a scientific journal which claims that fewer than 3 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to support the claim that the true proportion is less than 3 in ten thousand. B) There is not sufficient evidence to support the claim that the true proportion is greater than 3 in ten thousand. C) There is sufficient evidence to support the claim that the true proportion is greater than 3 in ten thousand. D) There is not sufficient evidence to support the claim that the true proportion is less than 3 in ten thousand. 8) Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. 9) A medical researcher claims that 10% of children suffer from a certain disorder. Identify the type I 9) error for the test. A) Reject the claim that the percentage of children who suffer from the disorder is equal to 10% when that percentage is actually 10%. B) Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 10% when that percentage is actually different from 10%. C) Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 10% when that percentage is actually 10%. D) Reject the claim that the percentage of children who suffer from the disorder is different from 10% when that percentage really is different from 10%. 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 10) A supplier of digital memory cards claims that no more than 1% of the cards are 10) defective. In a random sample of 600 memory cards, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the P-value for the indicated hypothesis test. 11) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%. A) 0.0524 B) 0.0048 C) 0.0262 D) 0.0024 11) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. 12) A public bus company official claims that the mean waiting time for bus number 14 12) during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method of testing hypotheses. Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. 13) Test the claim that the mean age of the prison population in one city is less than 26 years. 13) Sample data are summarized as n = 25, x = 24.4 years, and s = 9.2 years. Use a significance level of = 0.05. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 14) Various temperature measurements are recorded at different times for a particular city. 14) The mean of 20°C is obtained for 60 temperatures on 60 different days. Assuming that = 1.5°C, test the claim that the population mean is 22°C. Use a 0.05 significance level. 3 Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 15) The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 15) parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer. The levels, in ppm, are shown below. 0.31 0.47 0.19 0.72 0.56 0.91 0.29 0.83 0.49 0.28 0.31 0.46 0.25 0.34 0.17 0.58 0.19 0.26 0.47 0.81 Do the data provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm? Use a 0.05 significance level to test the claim that these sample levels come from a population with a mean greater than 0.4 ppm. Use the P-value method of testing hypotheses. Assume that the standard deviation of levels of the chemical in all such tomatoes is 0.21 ppm. 4 Answer Key Testname: CHAPTER 8 PRACTICE 1) B 2) C 3) B 4) A 5) D 6) C 7) B 8) A 9) A 10) H0 : p = 0.01. H1 : p > 0.01. Test statistic: z = 4.92. P-value: p = 0.0001. Critical value: z = 2.33. Reject null hypothesis. There is sufficient evidence to warrant rejection of the claim that no more than 1% are defective. Note: Since the term "no more than" is used, the translation is p 0.01. Therefore, the competing hypothesis is p > 0.01. 11) B 12) H0 : µ = 10 min. H1 : µ < 10 min. Test statistic: t = -4.427. P-value < 0.005. Reject H0 . There is sufficient evidence to support the claim that the mean is less than 10 minutes. = 0.05 Test statistic: t = -0.87 P-value: p = 0.1966 Critical value: t = -1.711 Because the test statistic, t > -1.711, we do not reject the null hypothesis. There is not sufficient evidence to support the claim that the mean age is less than 26 years. 14) H0 : µ = 22; H1 : µ 22. Test statistic: z = -10.33. P-value: 0.0002. Because the P-value is less than the significance level 13) of = 0.05, we reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the population mean temperature is 22°C. 15) H0 : µ = 0.4 ppm H1 : µ > 0.4 ppm Test statistic: z = 0.95 P-value: 0.1711 Do not reject H0 ; At the 5% significance level, the data do not provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm. 5

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