The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the α = 0.05 level, can it be concluded that the mean rainfall was below the reported average? What if α = 0.01? Assume the amount of summer rainfall follows a normal distribution.

a. State the null and alternate hypothesis.

b. State the p-value.

c. State alpha.

d. What is the decision?

e. I need a conclusion.

f. Answer any other questions asked in the problem.

 

(With step-by-step explanation please.)

a) H0?:μ=11.52

     H0?:μ<11.52

b) Test statistic= -9.973

  df=9

  P-value= 0.000

c) alpha= 0.01

d) Reject the null hypothesis

e) There is sufficient evidence to support the claim that the mean rainfall was below the reported average of 11.52 inches

Step-by-step explanation

a ) Testing the claim that the mean rainfall is less than 11:52 inches Null and alternative hypotheses Ho: u = 11.52 HI: U 2 11 . 52 b ) The test statistic &gt; since the population standard deviation is unknown, we use the t-distribution ( = 5c - 4 t = 7.42-11.52 1:3 t = - 9.973 -&gt; Degrees of freedom dof = n - 1 = (0 - 1 df = 9 * ) P-value = P ( t &lt; - 9 . 9 73 ) = 0.000 P- value = 0:000

c J . level of significance ( alpha ) &quot; = 0.01 Decision At aso.ol we reject the null hypothesis since the .. pvalue is less than ool e ) Conclusion There is sufficient evidence to support the claim that the mean raintall was below the reported value of 11:52 inches .