Question

(d) determine whether to reject ( h_0 ).
at the ( alpha = 0.10 ) level, (\boldsymbol{\text{reject}}) (\boldsymbol{\text{do not reject}}) the null hypothesis ( h_0 ).
at the ( alpha = 0.01 ) level, (\boldsymbol{\text{do not reject}}) (\boldsymbol{\text{reject}}) the null hypothesis ( h_0 ).
part: 4 / 5
part 5 of 5
(e) state a conclusion.
at the ( alpha = 0.10 ) level of significance, there (\boldsymbol{\text{is}}) (\boldsymbol{\text{is not}}) enough evidence to conclude that greater than 68% of emails are spam.
at the ( alpha = 0.01 ) level of significance, there (\boldsymbol{\text{is}}) (\boldsymbol{\text{is not}}) enough evidence to conclude that greater than 68% of emails are spam.

Explanation:

Step1: Recall Hypothesis Testing Logic

In hypothesis testing, if we reject \( H_0 \) at a significance level \( \alpha \), there is enough evidence for the alternative hypothesis. If we do not reject \( H_0 \), there is not enough evidence.

Step2: Analyze \( \alpha = 0.10 \)

From part (d), at \( \alpha = 0.10 \), we "reject" \( H_0 \). So, there is enough evidence for the alternative (greater than 68% spam).

Step3: Analyze \( \alpha = 0.01 \)

From part (d), at \( \alpha = 0.01 \), we "do not reject" \( H_0 \). So, there is not enough evidence for the alternative.

Answer:

At the \( \alpha = 0.10 \) level: is
At the \( \alpha = 0.01 \) level: is not