The January mean number of sunspots is recorded for a sequence of recent Januaries.

57.5 38.7 19.4 15.2 17.9 28.8

110.9 121.2 104.6 111.9 9.5 61.7

43.6 27.1 18.3 8.7 16.1 51.1

Use level of significance 5% to test for randomness about the median. Interpret the results.

What is the level of significance?

State the null and alternate hypotheses.

H₀: The numbers are not randomly mixed about the median.

H₁: The numbers are randomly mixed about the median.

H₀: The numbers are randomly mixed about the median.

H₁: The numbers are not randomly mixed about the median.

H₀: The numbers are randomly mixed about the mean.

H₁: The numbers are not randomly mixed about the mean.

H₀: The numbers are not randomly mixed about the mean.

H₁: The numbers are randomly mixed about the mean.

Find the sample test statisticR, the number of runs.

R=

Find the upper and lower critical values in Table 10 of Appendix II.c₁=c₂=

Conclude the test.

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

Interpret the conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the number of sunspots is not random about the median.

Fail to reject the null hypothesis, there is insufficient evidence that the number of sunspots is not random about the mean.

Fail to reject the null hypothesis, there is insufficient evidence that the number of sunspots is not random about the median.

Reject the null hypothesis, there is sufficient evidence that the number of sunspots is not random about the mean.