Gestational length, African American women, power. Suppose the average gestational length in African American women is actually 38.5 weeks. What was the power of the test described in Question 1 to detect this difference at α = 0.05 (two-sided)?

Work on the following problem set and show your work within the document. Use SPSS as needed.

Chapter 9

1. Gestational length, African American women, hypothesis test. Studies in the general population suggest that the gestational length of uncomplicated pregnancies varies according to a Normal distribution with μ = 39 weeks with σ = 2 weeks. A sample of 22 middle-class African American women demonstrates an average gestation length (Ẋ) of 38.5 weeks. Test whether the mean gestation period in the African American women is significantly different from the expected value of 39 weeks. Use a two-sided alternative hypothesis. Show all hypothesis testing steps.

2. Gestational length, African American women, power. Suppose the average gestational length in African American women is actually 38.5 weeks. What was the power of the test described in Question 1 to detect this difference at α = 0.05 (two-sided)?

3. Suppose a pizza place claims its average pizza delivery time is 30 minutes, but you believe it takes long than that.  What are your null and alternative hypotheses?

4. If the mean of a sample that contains 25 participants is equal to 82, the population mean is equal to 79 with a standard deviation of 15, what is the value of Z obt?

5. We test a technique for changing reading comprehension.  Without it, the population mean on a reading test is 220 with a standard deviation of 15.  An sample of 25 participants has a mean of 211.55.  Use a Z test and the 10 step process to determine if the technique changes reading comprehension scores. Use this as a sample to complete the rest.

Step 1: Null Hypothesis – There is no difference in reading comprehension scores between participants who use the new technique and those who don’t.

Step 2: Research Hypothesis – There is a difference in the scores of participants who use the new technique for reading comprehension.

Step 3: This test will be two-tailed

Step 4: The level of significance is .05

Step 5: Use the Z test

Step 6: N/A

Step 7: Z crit = -1.96 or +1.96

Step 8: If Z obt is beyond +1.96 or -1.96, I must reject the null and accept the research hypothesis.

Step 9: Z obt = -2.82

Step 10: There is sufficient evidence at the 5% level to support the claim that the alternative hypothesis represents the population.

6. We predict that learning statistics will increase a student’s IQ.  Those not learning statistics have a population mean of 100 with a standard deviation of 15.  For 25 statistics students, the mean is equal to 108.6.  Use a Z test and the 10 step process to determine if learning statistics increases a student’s IQ.

Step 1: Research Hypothesis?

Step 2: Null Hypothesis?

Step 3: One or two tails?

Step 4: Alpha level?

Step 5: What test?

Step 6: Degrees of Freedom? N/A

Step 7: Critical Value?

Step 8: Decision Rule?

Step 9: Finding?

Step 10: Conclusion?

7. We test whether a sample of 36 successful dieters are more or less satisfied with their appearance than in the population of non-dieters, where the population mean = 40 (standard deviation = 12). Use a Z test and the 10 step process to determine if there is a difference in satisfaction with appearance between dieters and non-dieters. The mean of the sample is 44.

Step 1: Research Hypothesis?

Step 2: Null Hypothesis?

Step 3: One or two tails?

Step 4: Alpha level?

Step 5: What test?

Step 6: Degrees of Freedom? N/A

Step 7: Critical Value?

Step 8: Decision Rule?

Step 9: Finding?

Step 10: Conclusion?

Chapter 10

1. Suppose an independent environmental group computes the gas mileage for a random sample of 100 new models of the same car make and model in order to make a statement about the gas mileage of this make and model. The results on these 100 cars include the following summary statistics:

· Sample mean mileage, 31.4 mpg

· Sample standard deviation: 1.2 mpg

· Sample median: 31.2 mpg

a. Assuming the gas mileage data is normally distributed, estimate a range of gas mileage for most (95%) of the cars of this make and model based on the sample results

b. Assuming the gas mileage data is normally distributed, estimate a 95% confidence interval for the mean gas mileage for all cars that are this make and model

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