Question

For each of the following problems: a. state the research and null hypotheses b. compute either the z- or t-statistic c. decide whether to use a one-tailed or two-tailed test d. determine the p-value for the hypothesis test e. decide whether there is evidence to reject the null hypothesis (use =0.05) f. Plus, be sure to explicitly answer the question included in the problem! 1. According to an article in The New York Times (5/12/2004), 18.7% of New York City adults smoked in 2003. You believe that fewer adults smoke now than they did ten years ago. Suppose you conduct a survey to determine this year’s rate. You randomly sample 76 New York City residents and discover that only 13 people in this group smoke. Do you have enough evidence to suggest that the percentage of smokers in New York City (as a whole—the population) is now less than 18.7%? 2. A large counseling center needs to evaluate a new experimental program designed for divorce counseling. A key feature of the program is its counselors, who are married couples working in teams. About half of all clients have been randomly assigned to this special program and half to the regular program. The proportion of cases that eventually ended in divorce are recorded for both. The results for random samples of couples from both programs are reported below. In terms of preventing divorce, would instituting the new program result in fewer divorces? Sample 1 (Special Program) Sample 2 (Regular Program) P1 = 0.56 P2 = 0.62 N1 = 79 N2 = 84 3. Nationally, the U.S. population as a whole watches 6.3 hours of TV per day. A random sample of 1,017 college students report watching an average of 5.9 hours per day with a standard deviation of 0.6. Do we have enough evidence to say that the amount of TV that college students watch is different than the national average? 4. Research shows that even for married couples in two-income households, women perform significantly more housework than men (see Hersh and Stratton 2000). You wish to replicate this study and you sample populations of married men and women, all of whom work fulltime outside the home. Housework (Y) is measured in hours and the standard deviations are significantly different from one another. Do your data below support the previous research findings (that women perform more housework)? Women Men 1 = 29.15 2 = 23.24 S1 = 4.12 S2 = 11.05 N1 = 57 N2 = 57

For each of the following problems:
a. state the research and null hypotheses
b. compute either the z- or t-statistic
c. decide whether to use a one-tailed or two-tailed test
d. determine the p-value for the hypothesis test
e. decide whether there is evidence to reject the null hypothesis (use =0.05)
f. Plus, be sure to explicitly answer the question included in the problem!

1. According to an article in The New York Times (5/12/2004), 18.7% of New York City adults smoked in 2003. You believe that fewer adults smoke now than they did ten years ago. Suppose you conduct a survey to determine this year’s rate. You randomly sample 76 New York City residents and discover that only 13 people in this group smoke. Do you have enough evidence to suggest that the percentage of smokers in New York City (as a whole—the population) is now less than 18.7%?

2. A large counseling center needs to evaluate a new experimental program designed for divorce counseling. A key feature of the program is its counselors, who are married couples working in teams. About half of all clients have been randomly assigned to this special program and half to the regular program. The proportion of cases that eventually ended in divorce are recorded for both. The results for random samples of couples from both programs are reported below. In terms of preventing divorce, would instituting the new program result in fewer divorces?

Sample 1 (Special Program) Sample 2 (Regular Program)
P1 = 0.56 P2 = 0.62
N1 = 79 N2 = 84

3. Nationally, the U.S. population as a whole watches 6.3 hours of TV per day. A random sample of 1,017 college students report watching an average of 5.9 hours per day with a standard deviation of 0.6. Do we have enough evidence to say that the amount of TV that college students watch is different than the national average?

4. Research shows that even for married couples in two-income households, women perform significantly more housework than men (see Hersh and Stratton 2000). You wish to replicate this study and you sample populations of married men and women, all of whom work fulltime outside the home. Housework (Y) is measured in hours and the standard deviations are significantly different from one another. Do your data below support the previous research findings (that women perform more housework)?

Women Men
1 = 29.15
2 = 23.24

S1 = 4.12 S2 = 11.05
N1 = 57 N2 = 57

Added by Haiden A.

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