Question

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  

Answer 1

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

Answer: Not rejected H0