Question

# The following hypotheses are given. H0: p ≤ 0.45 H1: p > 0.45 A sample of...

The following hypotheses are given.

H0: p ≤ 0.45

H1: p > 0.45

A sample of 140 observations revealed that

= 0.35. At the 0.10 significance level, can the null hypothesis be rejected?

a. State the decision rule. (Round the final answer to 3 decimal places.)

(Click to select)  Reject  Not reject  H0 and  (Click to select)  and accept  and reject  H1 if z >  or z <  .

b. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

Value of the test statistic

c. What is your decision regarding the null hypothesis?

(Click to select)  Not rejected  Rejected  H0

a. State the decision rule.

We are given

α = 0.10

Test is an upper tailed test.

So, critical Z value is given as below:

Z = 1.282

Reject H0 if z > 1.282.

b. Compute the value of the test statistic.

Test statistic formula is given as below:

Z = (p̂ - p)/sqrt(pq/n)

We are given

p̂ = 0.35

p = 0.45

q = 1 - p = 1 - 0.45 = 0.55

n = 140

Z = (0.35 - 0.45)/sqrt(0.45*0.55/140)

Z = -2.37835

Test statistic = -2.38

c. What is your decision regarding the null hypothesis?

For this test, we have

Test statistic = -2.38 < Critical value = 1.282

So, we do not reject the null hypothesis

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