Question

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.

Month	Jan.	Feb.	March	April	May	June
Madison	17.4	21.9	31.4	46.7	57.9	67.5
Juneau	22.3	27.8	31.7	38.5	46.7	52.6

Month	July	Aug.	Sept.	Oct.	Nov.	Dec.
Madison	71.5	69.5	60.9	51.4	35.1	22.9
Juneau	55.9	54.5	49.4	41.4	32.1	26.7

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: Distributions are different. H₁: Distributions are different.

H_o: Distributions are different. H₁: Distributions are the same.   

H_o: Distributions are the same. H₁: Distributions are different.

H_o: Distributions are the same. H₁: Distributions are the same.

(b) Compute the sample test statistic. (Use 2 decimal places.)

What sampling distribution will you use?

Student's t

chi-square    

uniform

normal

(c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

(d) Conclude the test?

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

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

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

Reject the null hypothesis, there is sufficient evidence that the temperature distribution differs in Juneau and Madison.

Fail to reject the null hypothesis, there is sufficient evidence that the temperature distribution differs in Juneau and Madison.  

  Fail to reject the null hypothesis, there is insufficient evidence that the temperature distribution differs in Juneau and Madison.

Reject the null hypothesis, there is insufficient evidence that the temperature distribution differs in Juneau and Madison.

Answer 1

(a) level of significance=0.05

Ho: Distributions are the same. H1: Distributions are different.

(b) test statistic:

What sampling distribution will you use?

Student's t

(c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

p-value=2P(t> 2.63|t₁₁)= 0.0234

(d) Conclude the test?

Since p-value<0.05, so

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

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

Reject the null hypothesis, there is sufficient evidence that the temperature distribution differs in Juneau and Madison.