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Chapter 8: Q3E (page 325)

For which of the given P-values would the null hypothesis be rejected when performing a level .05 test?

a. .001 b. .021 c. .078

d..047 e. .148

Short Answer

Expert verified

a) Reject the null hypothesis\({H_0}\).

b) Reject the null hypothesis\({H_0}\).

c) Fail to reject the null hypothesis\({H_0}\).

d) Reject the null hypothesis\({H_0}\).

e) Fail to reject the null hypothesis \({H_0}\).

Step by step solution

01

Step 1:Null hypothesis.

The null hypothesis, denoted by H0, is the claim that is initially assumed to be true (the 鈥減rior belief鈥� claim). The alternative hypothesis, denoted by Ha, is the assertion that is contradictory to H0.

The null hypothesis will be rejected in favor of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0.

02

Step 2:Solution for part a).

Given that,

\(\begin{array}{l}P = 0.001\\\alpha = 0.05\end{array}\)

If the \(P\)-value is less than the significance level \(\alpha \), then reject the null hypothesis

\({H_0}\), else we fail to reject the null hypothesis \({H_0}\).

\(P = 0.001 < 0.05\)

In the given \(P < \alpha \), so, it rejects the \({H_0}\).

Reject the null hypothesis \({H_0}\).

03

Step 3:Solution for part b).

Given that,

\(\begin{array}{l}P = 0.021\\\alpha = 0.05\end{array}\)

If the \(P\)-value is less than the significance level \(\alpha \), then reject the null hypothesis \({H_0}\), else we fail to reject the null hypothesis \({H_0}\).

\(P = 0.021 < 0.05\)

In the given \(P < \alpha \), so, it rejects the \({H_0}\).

Reject the null hypothesis \({H_0}\).

04

Step 4:Solution for part c).

Given that,

\(\begin{array}{l}P = 0.078\\\alpha = 0.05\end{array}\)

If the \(P\)-value is less than the significance level \(\alpha \), then reject the null hypothesis \({H_0}\), else we fail to reject the null hypothesis \({H_0}\).

\(P = 0.078 > 0.05\)

In the given \(P > \alpha \), so, it fails to rejects the \({H_0}\).

Fail to reject the null hypothesis \({H_0}\).

05

Step 5:Solution for part d).

Given that,

\(\begin{array}{l}P = 0.047\\\alpha = 0.05\end{array}\)

If the \(P\)-value is less than the significance level \(\alpha \), then reject the null hypothesis \({H_0}\), else we fail to reject the null hypothesis \({H_0}\).

\(P = 0.047 < 0.05\)

In the given \(P < \alpha \), so, it rejects the \({H_0}\).

Reject the null hypothesis \({H_0}\).

06

Step 6:Solution for part e).

Given that,

\(\begin{array}{l}P = 0.148\\\alpha = 0.05\end{array}\)

If the \(P\)-value is less than the significance level \(\alpha \), then reject the null hypothesis \({H_0}\), else we fail to reject the null hypothesis \({H_0}\).

\(P = 0.148 > 0.05\)

In the given \(P > \alpha \), so, it fails to rejects the \({H_0}\).

Fail to reject the null hypothesis \({H_0}\).

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