Question

The following hypotheses are given.

*H*_{0}: *p* ≤ 0.45

*H*_{1}: *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 *H*_{0} and (Click to
select) and accept and
reject *H*_{1} 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 *H*_{0 }

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

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