Question

Trap-spacing measurements (in meters) for a sample of seven terms of red spiny lobster fishermen are reproduced as following: 93, 99, 105, 94, 82, 70, 86. Suppose you want to determine if the true value of ? differs from 95 meters. (a) Specify the null and alternative hypotheses for this test. (2) (b) Computer the value of the test statistics. (2) (c) Find the approximate p-value of the test. (2) (d) Select a value of ?, the probability of a Type I error. Interpret this value in the words of the problem. (2) (e) Give the appropriate conclusion, based on the results of parts (c) and (d). (2) (f) What condition must be satisfied for the test results to be valid? (2) (g) Find a 95% confidence interval for ?. Does this interval support your conclusion in part (e)?

Answer 1

a) Null and alternative hypotheses

Ho : = 95

Ha : 95

b) From the given data

n = sample size = 7 , xbar = sample mean = 89.86 , s = 11.63

Test statistic t

t =( xbar - )/(s/√n)

t = 89.86 - 95/(11.63/√7)

t = -1.17

c) p-value for t = -1.17 and d.f = n -1= 6

p-value = 2 *P( t < -1.17) d.f = 6

P-value = 0.2864

d) level of significance a = 0.05

e) decision rule : If p-value < a we reject the null hypothesis , otherwise we fail to Reject the null hypothesis.

Our p-value = 0.2864 > 0.05

Conclusion : Fail to reject the null hypothesis Ho , there is no sufficient evidence true value of population mean differs from 95