Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archaeologists think sunspot activity may somehow be related to prolonged periods of drought in the southwestern United States. Let x be a random variable representing the average number of sunspots observed in a 4-week period. A random sample of 40 such periods from Spanish colonial times gave the following data. The sample mean is x-bar = 47.0. Previous studies of sunspot activity during this period indicate that the population standard deviation, sigma, is 35.
It is thought that for thousands of years, the mean number of sunspots per 4-week period was about mu = 41. Sunspot activity above this level may (or may not) be linked to gradual climate change. Do the data indicate that the mean sunspot activity during the Spanish colonial period was higher than 41? Use significance level alpha = 0.05.
1) Establish the null and the alternative hypotheses.
2) What distribution do we use for the sample test statistic?
3) Determine the Rejection Region, critical value(s), the form of the test (left, right, or two-tailed test).
4) Compute the z-value of the sample test statistic x-bar.
5) Interpret the results in the context of the problem.
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