The following data are paired by date. Letxandybe random variables representing wind direction at 5 a.m. and 5 p.m., respectively (units are degrees on a compass, with 0representing true north). The readings were taken at seeding level in a cloud seeding experiment. A random sample of days gave the following information

.x 171 140 197 224 58 175 257 72 172

y 145 142 217 125 40 245 218 35 147

x 205 265 110 193 180 190 94 8 96

y 219 218 100 170 245 117 140 99 67

Use the sign test with a 5% level of significance to test the claim that the distributions of wind directions at 5 a.m. and 5 p.m. are different. Interpret the results.

What is the level of significance?

State the null and alternate hypotheses.

H₀: Distributions are different.H₁: Distributions are the same.

H₀: Distributions are the same.H₁: Distributions are the same.

H₀: Distributions are the same.H₁: Distributions are different.

H₀: Distributions are different.H₁: Distributions are different.

Compute the sample test statistic. (Round your answer to two decimal places.)

What sampling distribution will you use?

chi-square

uniform

normal

Student'st

Find theP-value of the sample test statistic. (Round your answer to four decimal places.)

Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the wind directions at 5 a.m. and 5 p.m. are different.

Fail to reject the null hypothesis, there is sufficient evidence that the wind directions at 5 a.m. and 5 p.m. are different.

Reject the null hypothesis, there is insufficient evidence that the wind directions at 5 a.m. and 5 p.m. are different.

Reject the null hypothesis, there is sufficient evidence that the wind directions at 5 a.m. and 5 p.m. are different.