Question

A research center claims that at most 76​% of adults in a certain country think that drivers are safer using​ hands-free cell phones instead of using​ hand-held cell phones. In a random sample of 200 adults from that​ country 79​% think that drivers are safer using​hands-free cell phones instead of using​ hand-held cell phones. At

alphaαequals=0.01​, is there enough evidence to reject the​ center's claim? Complete parts​ (a) through​ (e) below.

What is the​ claim?

Identify Upper H 0H0 and Upper H Subscript aHa.

Find the critical​ value(s) and identify the rejection​ region(s). The critical​ value(s) is/are z 0z0

What​ is/are the rejection​ region(s)? Select the correct choice below and fill in the answer​ box(es) to complete your choice

Find the standardized test statistic z.

Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

Answer 1

Solution:

Given:
Sample Size = n= 200
Sample proportion =
Level of significance=

Part a) What is the​ claim?

At most 76​% of adults in a certain country think that drivers are safer using​ hands-free cell phones instead of using​ hand-held cell phones.

Part b) Identify H0 and Ha

Part c) Find the critical​ value(s) and identify the rejection​ region(s).

Since this is right tailed test, find Area

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_critical = 2.33

Rejection region:

Reject H0, if z test statistic value > 2.33

Part d) Find the standardized test statistic z.

Part e) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

Since z test statistic value = z = 0.99 < z critical value = 2.33, we fail to reject null hypothesis H0.

Thus there is sufficient evidence to support a research center claims that at most 76​% of adults in a certain country think that drivers are safer using​ hands-free cell phones instead of using​ hand-held cell phones.