Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archacologists think sunspot activity may somehow be related to prolonged periods of drought in the southern United States. Let x be a random variable representing the average number of sunspots observed in a four-week period. A random sample of 40 such periods from Spanish colonial times gave a sample mean, 1 = 47.0. Previous studies of sunspot activity during this period indicate that a = 35. It is thought that for thousands of years, the mean number of sunspots per 4-week period was about ji = 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 a = 0.05 (a) Establish the null (H) and alternative (H) hypotheses. (1) What distribution do we use for the sample test statistic? The normal (2) or the student'st distribution. Explain. (c) Compute the test statistic? (d) Find the P-value of the test statistic. (e) Based on the P-value and the level of significance, do you reject or fail to reject H,? Explain (1) Interpret your results in the context of the problem. Statesi Focus E
