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# Hypothesis testing problems

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13. For each of the following:
(a) State which two populations are being compared

(b) State the research hypothesis
(c) State the null hypothesis
(d) Say whether you should use a one-tailed or two-tailed test and why.

i. In an experiment, people are told to solve a problem by focusing on the details.
Is the speed of solving the problem different for people who get such instructions compared to the speed for people who are given no special instructions?

ii. Based on anthropological reports in which the status of women is scored on a
10-point scale, the mean and standard deviation across many cultures are known. A new culture is found in which there is an unusual family arrangement.
The status of women is also rated in this culture. Do cultures with the unusual family arrangement provide higher status to women than cultures in general?

iii. Do people who live in big cities develop more stress-related conditions than people in general?

16. A researcher wants to test whether a certain sound will make rats do worse on learning tasks. It is known that an ordinary rat can learn to run a particular maze correctly in 18 trials, with a standard deviation of 6. (The number of trials to learn this maze is normally distributed.) The researcher now tries an ordinary rat in the maze, but with the sound. The rat takes 38 trials to learn the maze.

(a) Using the .05 level, what should the researcher conclude?
Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.

(b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).

20. In an article about anti-tobacco campaigns, Siegel and Biener (1997) discuss the results of a survey of tobacco usage and attitudes, conducted in Massachusetts in 1993 and 1995; Table 4-4 shows the results of this survey. Focusing on just the first line (the percentage smoking 25 cigarettes daily), explain what this result means to a person who has never had a course in statistics. (Focus on the meaning of this result in terms of the general logic of hypothesis testing and statistical significance.)

Table 4-4 Selected Indicators of Change in Tobacco Use, ETS Exposure, and Public Attitudes toward Tobacco Control Policies-Massachusetts, 1993-1995
1993 1995
Percentage smoking >25 cigarettes daily 24 10*

Percentage smoking <15 cigarettes daily 31 49*

Percentage smoking within 30 minutes of waking 54 41

Environmental Tobacco Smoke Exposure

Percentage of workers reporting a smoke free worksite 53 65*

Mean hours of ETS exposure at work during prior week 4.2 2.3*

Percentage of homes in which smoking is banned 41 51*

Attitudes Toward Tobacco Control Policies

Percentage supporting further increase in tax on
tobacco with funds earmarked for tobacco control 78 81

Percentage believing ETS is harmful 90 84

Percentage supporting ban on vending machines 54 64*

Percentage supporting ban on support of sports and cultural
events by tobacco companies 59