1. A random sample of 20 observations produced a sample mean of 9.5. Find the critical and observed z-values for each of the following and test each hypothesis at α = 0.05. Write a separate conclusion for each hypothesis. The underlying population standard deviation is known to be 3.5 and the population distribution is normal:
a. H0: µ = 8.75; H1: µ ≠ 8.75
b. H0: µ = 8.75; H1: µ > 8.75
2. Police on a heavily traveled highway claim that the average car exceeds the speed limit of 65 mph by at least 10 mph. A random sample of 50 cars is evaluated and found to have an average speed of 82.5 mph with a standard deviation for this sample of 7.3 mph. Determine the 95% confidence interval for this example, state the null and alternative hypothesis about the police's claim and determine if the claim is indeed correct at a significance level of α = 0.05.
3. The article entitled "Effect of metformin therapy on 2-h post-glucose insulin levels in patients of polycystic ovarian syndrome" by Saxena et al. discussed the influence of metformin on insulin levels in women with polycystic ovarian syndrome (POCS),
Summarize the article in terms of the statistics that were used and calculate the following statistics for i) the body mass index, ii) the FSH levels, and iii) the mean hirsutism scores:
a. The 95% and 99% confidence intervals.
b. Test the null and alternative hypothesis that the after treatment results are significantly different from the before treatment results.