The Focus Problem at the beginning of this chapter asks you to use a sign test with a 5% level of signi­ficance to test the claim that the overall temperature distribution of Madison, Wisconsin, is different (either way) from that of Juneau, Alaska. The monthly average data (in °F) are as follows.

What is your conclusion?

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Compute the sample test statistic. What is the sampling distribution?

(c) Find the P-value of the sample test statistic.

(d) Conclude the test.

(e) Interpret the conclusion in the context of the application.

Month Madison Juneau Jan. 17.5 22.2 Feb. 21.1 27.3 March 31.5 31.9 April 46.1 38.4 May 57.0 46.4 June 67.0 52.8 Month Madison Juneau July 71.3 55.5 Aug. 69.8 54.1 Sept. 60.7 49.0 Oct 51.0 41.5 Nov. 35.7 32.0 Dec. 22.8 26.9