Complete the below:
Q1: 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 x¯ = 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 x¯ = 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 x¯ = 4.8 gets smaller (more significant) as the sample size increases.
b) For each test, sketch the Normal curve for the sampling distribution of x¯ when H0 is true. This curve has a mean 5.0 and standard deviation 0.5/ √n.
Make the observed x¯ = 4.8 on each curve. (If you use the applet, you can just copy the curves displayed by the applet. The same result x¯ = 4.8 gets more extreme on the sampling distribution as the sample size increases.
Q2: 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?