#1
Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that results in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has a pH of 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviation σ = 0.5. A sample of n days finds that the mean pH is x̄ = 4.8. Is this good evidence that the mean pH μ for all rainy days is less than 5.0? The answer depends on the size of the sample.

Either by hand or using the P-Value of a Test of Significance applet, carry out three tests of:

H₀: μ = 5.0
Ha: μ < 5.0

Use σ = 0.5 and x̄ = 4.8 in all three tests. But use three different sample sizes, n = 5, n = 15, and n = 40.

a) What are the P-values for the three tests? The P-value of the same result x̄ = 4.8 gets smaller (more significant) as the sample size increases.

b) For each test, sketch the Normal curve for the sampling distribution of x̄ when H₀ is true. This curve has a mean 5.0 and standard deviation 0.5/ √n. Make the observed x̄ = 4.8 on each curve. (If you use the applet, you can just copy the curves displayed by the applet. The same result x̄ = 4.8 gets more extreme on the sampling distribution as the sample size increases.

#2
Suppose that scores of men aged 21 to 25 years on the quantitative part of the National Assessment of Educational Progress (NAEP) test follow a Normal distribution with standard deviation σ = 60. You want to estimate the mean score within ±10 with 90% confidence. How large an SRS of scores must you choose?

Suggest one psychological research question that could be answered by each of the following types of statistical test:
* z test
* t test for independent samples, and t test for dependent samples

Is there an alternative test to the chi squared test? What if my results give an expected frequency below 5, which stats book states that these should be treated with caution? Is there a more appropriate stat test which would be more accurate in working out the significance of the results?

A research organization has collected the following data on household size and telephone ownership for 200 U.S. households at the 0.05 level, are the two variables independent? Based on the chi-square table, what is the most accurate statement that can be made about the p-value for the test?

A medical test for malaria is subject to some error. Given a person who has malaria, the
probability that the test will fail to reveal the malaria is 0.06. Given a person who does not
have malaria, the test will correctly identify that the person does not have malaria with
probability 0.91. In a particular area, 20% of the

Consider the following hypothesis test: H0: mean greater than or equal to 5 vs. H1: mean < 5. Suppose that you take a sample and conduct the test. You conclude that you can reject the null hypothesis.
What can you say about the results of the hypothesis test: H0: mean = 5 vs. H1: mean not equal to 5 tested using the same

Collapse the response categories in the following table so that it meets the assumption of the chi-square test; then perform the test.
OWNERSHIP
Education Owners Non-owners
Less than grade 8

Perform a chi-square test on the following data:
(a) Regulation is the best way to ensure a safe workplace.
Managers Blue-Collar Workers
Agree 58 66
Disagree