To study the impact of the crisis on different cultural sectors, you have collected information on the number of performances from several artists during the years 2007 (240 artists) and 2012 (191 artists). The following table indicates the mean, standard deviation and number of observations for each of the two years:

Year Mean Standard dev n

2007 13.287500 18.41356 240

2012 8.664921 13.09772 191

(a) Indicate the null and alternative hypotheses, and compute the value of the test statistic.

(b) Complete the hypothesis test at a significance level of 5%

If we study the evolution of the variance, we obtain the following results corresponding to the comparison of the variances in the numbers of performances for the years 2007 and 2012:

F test to compare two variance

F=0.506, num df=190, denom df=239, p-value=6.551e-07

alternative hypothesis: true ratio of variances is less than 1

95 percent confidence interval:

0.0000000 0.6357257

sample estimates:

ratio of variances

0.5059596

(c) Indicate the null and alternative hypotheses, and compute the value of the test statistic.

(d) Complete the hypothesis test at a significance level of 5%.