Calculating Power Consider a hypothesis test of the claim

Problem 1BSC M and MS and Aspirin A package label includes a claim that the mean weight of the M and MS is 0.8535 g, and another package label includes the claim that the mean amount of aspirin in Bayer tablets is 325 mg. Which has more serious implications: rejection of the M and M claim or rejection of the aspirin claim? Is it wise to use the same significance level for hypothesis tests of both claims?

Problem 2BSC . Estimates and Hypothesis Tests Data Set 20 in Appendix B includes sample weights of the M and MS referenced in Exercise 1. We could use methods of Chapter 7 for making an estimate, or we could use those values to test some claim. What is the difference between estimating and hypothesis testing?

Problem 3BSC Mean Body Temperature A formal hypothesis test is to be conducted using the claim that the mean body temperature is equal to 98.6°F. a. What is the null hypothesis, and how is it denoted? b. What is the alternative hypothesis, and how is it denoted? c. What are the possible conclusions that can be made about the null hypothesis? d. Is it possible to conclude that “there is sufficient evidence to support the claim that the mean body temperature is equal to 98.6°F”?

Problem 4BSC Interpreting P-value When the clinical trial of the XSORT method of gender selection is completed, a formal hypothesis test will be conducted with the alternative hypothesis of p > 0.5, which corresponds to the claim that the XSORT method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you are responsible for developing the XSORT method and you want to show its effectiveness, which of the following T-values would you prefer: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?

Stating Conclusions About Claims. a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: 20% of adults smoke. A recent Gallup survey of 1016 randomly selected adults showed that 21% of the respondents smoke.

Problem 6BSC do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: When parents use the XSORT method of gender selection, the proportion of baby girls is greater than 0.5. The latest actual results show that among 945 babies born to couples using the XSORT method of gender selection, 879 were girls.

Problem 7BSC do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: The mean pulse rate (in beats per minute) of adult females is 76 or lower. For the random sample of adult females in Data Set 1 from Appendix B, the mean pulse rate is 77.5.

Problem 8BSC do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: The standard deviation of pulse rates of adult women is at least 50. For the random sample of adult females in Data Set 1 from Appendix B, the pulse rates have a standard deviation of 11.6.

Problem 9BSC refer to the exercise identified. Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads(because it is easy to get 11 heads in 20 flips by chance with a fair coin). Exercise do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: 20% of adults smoke. A recent Gallup survey of 1016 randomly selected adults showed that 21% of the respondents smoke.

Problem 10BSC refer to the exercise identified. Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads(because it is easy to get 11 heads in 20 flips by chance with a fair coin). Exercise do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: When parents use the XSORT method of gender selection, the proportion of baby girls is greater than 0.5. The latest actual results show that among 945 babies born to couples using the XSORT method of gender selection, 879 were girls.

Problem 11BSC refer to the exercise identified. Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads(because it is easy to get 11 heads in 20 flips by chance with a fair coin). Exercise do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: The mean pulse rate (in beats per minute) of adult females is 76 or lower. For the random sample of adult females in Data Set 1 from Appendix B, the mean pulse rate is 77.5.

Problem 12BSC refer to the exercise identified. Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads(because it is easy to get 11 heads in 20 flips by chance with a fair coin). Exercise do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. Claim: The standard deviation of pulse rates of adult women is at least 50. For the random sample of adult females in Data Set 1 from Appendix B, the pulse rates have a standard deviation of 11.6.

Problem 13BSC find the value of the test statistic.(Refer to Table 8-2 to select the correct expression for evaluating the test statistic.) Community Involvement Claim: Three-fourths of all adults believe that it is important to be involved in their communities. Based on a USA Today!Gallup poll of 1021 randomly selected adults, 89% believe that it is important to be involved in their communities.

Problem 14BSC find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.) Tax Returns Claim: Among those who file tax returns, less than one-half file them through an accountant or other tax professional. A Fellowes survey of 1002 people who file tax returns showed that 48% of them file through an accountant or other tax professional.

Problem 15BSC find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.) White Blood Cell Count Claim: For adult females, the standard deviation of their white blood cell counts is equal to 5.00. The random sample of 40 adult females in Data Set 1 from Appendix B has white blood cell counts with a standard deviation of 2.28.

Problem 16BSC find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.) white Blood Cell Count Claim: For adult females, the mean of their white blood cell counts is equal to 8.00. The random sample of 40 adult females in Data Set 1 from Appendix B has white blood cell counts with a mean of 7.15 and a standard deviation of 2.28. (The population standard deviation ? is not known.)

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) The test statistic of z = 2.00 is obtained when testing the claim that p > 0.5 . ________________ Equation Transcription: Text Transcription: alpha=0.05 z=2.00 p>0.5

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) The test statistic of z = ? 2.00 is obtained when testing the claim that p < 0.5 . ________________ Equation Transcription: Text Transcription: =0.05 z=-2.00 p<0.5

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) The test statistic of z = ? 1.75 is obtained when testing the claim that p = 1 / 3 . Equation Transcription: Text Transcription: alpha=0.05 z = ? 1.75 p = 1 / 3

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) The test statistic of z = 1.50 is obtained when testing the claim that \(\mathrm {p\ne 0.25}\) . Equation Transcription: Text Transcription: alpa=0.05 z = 1.50 p {not=} 0.25

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) With \(\mathrm {H\ 1:p\ne 0.25}\) , the test statistic is z = ? 1.23 . ________________ Equation Transcription: Text Transcription: alpha=0.05 H 1:p {not=} 0.25 z=-1.23

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) With \(\mathrm {H\ 1:p\ne 2\ /\ 3}\) , the test statistic is z = 2.50 . Equation Transcription: Text Transcription: alpha=0.05 H 1:p{not=}2/3 z=2.50

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) With H 1 : p < 0.6 , the test statistic is z = ? 3.00 . Equation Transcription: Text Transcription: alpha=0.05 H 1:p<0.6 z=-3.00

Finding P­-Values and Critical Values. In Exercises 17–24, assume that the significance level is \(\alpha=0.05\) ; use the given statement and find the P­-value and critical values. (See Figure 8­4.) With H 1 : p > 7 / 8 , the test statistic is z = 2.88 . Equation Transcription: Text Transcription: alpha=0.05 H 1:p>7/8 z=2.88

Problem 25BSC assume a significance level of ? = 0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) b. Without using technical terms, state a final conclusion that addresses the original claim. Original claim: The percentage of blue M and MS is greater than 5%. The hypothesis test results in a P-value of 0.0010.

Problem 26BSC assume a significance level of ? = 0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) b. Without using technical terms, state a final conclusion that addresses the original claim. Original claim: Fewer than 20% of M and M candies are green. The hypothesis test results in a P-value of 0.0721.

Problem 27BSC assume a significance level of ? = 0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) b. Without using technical terms, state a final conclusion that addresses the original claim. Original claim: Women have heights with a mean equal to 160.00 cm. The hypothesis test results in a P-value of 0.0614.

Problem 28BSC assume a significance level of ? = 0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) b. Without using technical terms, state a final conclusion that addresses the original claim. Original claim: Women have heights with a standard deviation equal to 5.00 cm. The hypothesis test results in a P-value of 0.0055.

Problem 29BSC use the given information to answer the following: a. Identify the null hypothesis and the alternative hypothesis. b. What is the value of a? c. What is the sampling distribution of the sample statistic? d. Is the test two-tailed, left-tailed, or right-tailed? e. What is the value of the test statistic? f. What is the P-value? g. What is the critical value? h. What is the area of the critical region? Gender Selection A 0.01 significance level is used for a hypothesis test of the claim that when parents use the XSORT method of gender selection, the proportion of baby girls is greater than 0.5- Assume that sample data consist of 55 girls born in 100 births, so the sample statistic of 0.55 results in a z score that is 1.00 standard deviation above 0.

Problem 30BSC use the given information to answer the following: a. Identify the null hypothesis and the alternative hypothesis. b. What is the value of a? c. What is the sampling distribution of the sample statistic? d. Is the test two-tailed, left-tailed, or right-tailed? e. What is the value of the test statistic? f. What is the P-value? g. What is the critical value? h. What is the area of the critical region? Gender Selection A 0.05 significance level is used for a hypothesis test of the claim that when parents use the XSORT method of gender selection, the proportion of baby girls is different from 0.5. Assume that sample data consist of 55 girls born in 100 births, so the sample statistic of 0.55 results in a z score that is 1.00 standard deviation above 0.

Problem 31BSC identify expressions that identify the type I error and the type II error that correspond to the given claim.(Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.) The proportion of people who write with their left hand is equal to 0.1.

Problem 32BSC identify expressions that identify the type I error and the type II error that correspond to the given claim.(Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.) The proportion of gamblers who consistently win in casinos is equal to 0.001.

Problem 33BSC identify expressions that identify the type I error and the type II error that correspond to the given claim.(Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.) The proportion of female statistics students is greater than 0.5.

Problem 34BSC Type I and Type II Errors. In Exercises, identify expressions that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.) The proportion of husbands taller than their wives is less than 0.9.

Problem 35BB Interpreting Power Chantix tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.

Calculating Power Consider a hypothesis test of the claim that the MicroSort method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p > 0.5 . Assume that a significance level of \(\alpha=0.05 \) is used, and the sample is a simple random sample of size n = 64. a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when it is false. (Hint: With a 0.05 significance level, the critical value is z = 1.645 , so any test statistic in the right tail of the accompanying top graph is in the rejection region where the claim is supported. Find the sample proportion \(\mathrm p\ ^\wedge\) in the top graph, and use it to find the power shown in the bottom graph.) b. Explain why the red-­shaded region of the bottom graph represents the power of the test. Equation Transcription: Text Transcription: p>0.5 alpha=0.05 n=64 z=1.645 p ^{wedge} =0.05 p=0.5 z=1.645 beta p=0.65

Problem 37BB Finding Sample Size to Achieve Power Researchers plan to conduct a test of a gender-selection method. They plan to use the alternative hypothesis of H1 : p > 0.5 and a significance level of ? = 0.05. Find the sample size required to achieve at least 80% power in detecting an increase in p from 0.5 to 0.55. (This is a very difficult exercise. Hint: See Exercise.) Exercise Calculating Power Consider a hypothesis test of the claim that the MicroSort method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p > 0.5. Assume that a significance level of ? = 0.05 is used, and the sample is a simple random sample of size n = 64.