Studdy AI Logo
Math  /  Data & Statistics

QuestionExercise A survey found the 21%21 \% of adults never exercise at all. A researcher selected a random sample of 120 adults and found that 21 adults said that they do not exercise at all. At α=0.05\alpha=0.05, is there sufficient evidence that less than 21%21 \% of adults do not exercise at all? Use the critical value method. Do not round intermediate steps.
Part 1 of 5 (a) State the hypotheses and identify the claim. H0:p=0.21H1:p<0.21\begin{array}{l} H_{0}: p=0.21 \\ H_{1}: p<0.21 \end{array} not claim claim
This hypothesis test is a □\square one-tailed test.
Part: 1/51 / 5 □\square
Part 2 of 5 (b) Find the critical value. Round the answer to at least two decimal places.
The critical value is □\square .

Studdy Solution

STEP 1

1. We are conducting a hypothesis test for a population proportion.
2. The null hypothesis is H0:p=0.21 H_0: p = 0.21 .
3. The alternative hypothesis is H1:p<0.21 H_1: p < 0.21 .
4. The significance level is α=0.05\alpha = 0.05.

STEP 2

1. Identify the type of test.
2. Determine the critical value for the test.

STEP 3

Identify the type of test.
Since the alternative hypothesis is H1:p<0.21 H_1: p < 0.21 , this is a left-tailed test.

STEP 4

Determine the critical value.
For a left-tailed test at α=0.05\alpha = 0.05, we find the critical value using the standard normal distribution (Z-distribution).
The critical value zα z_{\alpha} corresponds to the point where the cumulative probability is 0.05 0.05 .
Using a Z-table or calculator, the critical value for α=0.05\alpha = 0.05 is approximately:
zα=−1.645 z_{\alpha} = -1.645
The critical value is:
−1.645 \boxed{-1.645}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord