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Hypothesis testing of proportions

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Section 9.3. Q12. Married Adults. In a recent year, 125.8 million adults, or 58.6% of the adult American population, were married. In a New England town, a simple random sample of 1,445 adults includes 56.0% who are married. Use a 0.05 significance level to test the claim that this sample comes from a population with a married percentage of less than 58.6%.

Q12a. The null hypothesis

Q12b. The alternative hypothesis

A.    p<58.6%.

B.    p=58.6%

C.    p>58.6%

Q12c. The standard score (z-score) of the sample proportion:

A.    -1.01

B.    -1.51

C.    -2.01

D.    -2.51

Q12d. The p-value:

A.    0.156

B.    0.066

C.    0.022

D.    0.006

Q12e: Your conclusion:

A.    Reject the null hypothesis. There is evidence to support the claim this sample comes from a population with a married percentage of less than 58.6%.

B.    Do not reject the null hypothesis. There is no evidence to support the claim this sample comes from a population with a married percentage of less than 58.6%.

Confidence Interval for population mean

Section 10.1.

Q12. SAT Scores. A simple random sample of SAT scores is obtained, and the population has a distribution that is approximately normal. The sample statistics are n =41, sample mean =1503.  Sample standard deviation s=352. Construct the 95% confidence interval estimate of the population mean.

Q12a. 95% Confidence interval for the population mean

A.    813,   2193

B.    1151, 1855

C.    1395, 1611

Q12b. The following statement is correct or wrong?

If we repeat the process of obtaining samples and constructing confidence intervals, in the long run 95% of the confidence intervals will contain the true population mean.

A.    Correct

B.    Wrong

In we repeat the process of obtaining samples and calculating sample means, in the long run 95% of the sample means will fall to this 95% confidence interval.

A.    Correct

B.    Wrong

We are 95% confidence that this confidence interval will cover the true population mean.

A.    Correct

B.    Wrong

Hypothesis testing of population mean

Q22. Pulse Rates. One of the authors claimed that his pulse rate was lower than the mean pulse rate of statistics students. The author’s pulse rate was measured and found to be 60 beats per minute, and the 20 students in his class measured their pulse rates. The 20 students had a mean pulse rate of 74.5 beats per minute, and their standard deviation was 10.0 beats per minute. Is there sufficient evidence to support the claim that the mean pulse rate of statistics students is greater than 60 beats per minute? Use a 0.05 significance level.

Q22a. The null hypothesis

A.    Mean pulse is 74.5

B.    Mean pulse > 74.5

C.    Mean pulse is 60

D.    Mean pulse >60

Q22b. The alternative hypothesis

A.    Mean pulse is 74.5

B.    Mean pulse > 74.5

C.    Mean pulse is 60

D.    Mean pulse >60

Q22c. The test statistic

A.    1.485

B.    2.485

C.    4.485

D.    6.485

Q22d. Critical value

A.    1.729

B.    1.812

C.    1.833

D.    2.228

Q22e. The p-value is

A.    <0.001

B.    0.01

C.    0.05

D.    >0.05

Q22f: Hypothesis testing result:

A.    Reject the null hypothesis

B.    Do not reject the null hypothesis

Q22g: Conclusion

A.    There is sufficient evidence to support the claim

B.    There is no sufficient evidence to support the claim

Hypothesis Testing with Two-Way Tables

Section 10.2 Q18. Drinking and Pregnancy. A simple random sample of 1,252 pregnant women under the age of 25 includes 13 who were drinking alcohol during their pregnancy. A simple random sample of 2,029 pregnant women of age 25 and over includes 37 who were drinking alcohol during their pregnancy. (The data are based on results from the U.S. National Center for Health Statistics.) Use a 0.05 significance level to test the claim that the age category (under 25 and 25 or over) is independent of drinking during pregnancy.

Q18a. State the null hypothesis

A.    Age category is independent of drinking during pregnancy

B.    Age category is not independent of drinking during pregnancy

Q18b. State the alternative hypothesis.

A.    Age category is independent of drinking during pregnancy.

B.    Age category is not independent of drinking during pregnancy.

Q18c. Find the value of the Chi-square test statistic:

A.    0.181

B.    1.181

C.    2.181

D.    3.181

Q18d. Use the given significance level to find the Chi-square critical value

A.    2.07

B.    2.71

C.    3.84

D.    5.02

Q18e. Hypothesis testing result

A.    Reject the null hypothesis

B.    Do not reject the null hypothesis

Q18f. State the conclusion that addresses the original claim.

A.    There is enough evidence to reject the independence of the age category and drinking in pregnancy.

B.    There is no enough evidence to reject the independence of the age category and drinking in pregnancy.

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