Question

2. 7.4 QUESTION 5 A research center claims that at most 77% 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 150 adults from that country, 80% think that drivers are safer using hands-free cell phones instead of using hand-held cell phones. At αequals=0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. b.

(a)Identify HO and HA

(b) Find the critical value(s) and identify the rejection region(s).

The critical value(s) is/are z 0= nothing. . What is/are the rejection region(s)?

Select the correct choice below and fill in the answer box(es) to complete your choice.

c. Find the standardized test statistic z.

d) Decide whether to reject or fail to reject the null hypothesis and

(e) interpret the decision in the context of the original claim. ______H0. There is _________ enough evidence at the __% level of significance to ________the centers claim that ____of ______ think that…..

Answer 1

H0: p = 0.77
Ha: p > 0.77

b)
This is right tailed test, hence critical values will be on right
z-critical = 2.33

c)
pcap = 0.8
n = 150
SE = sqrt(p * (1-p) / n)
SE = sqrt(0.77 * 0.23 / 150)
SE = 0.0344

test statistic,
z = (pcap - p)/SE
z = (0.8 - 0.77)/0.0344
z = 0.8721

d)
As test statistic < critical value, fail to reject H0

e)
Reject H0. There is not enough evidence at the 1% level of significance to conclude that the centers claim that 77% of adults in a certain country think that drivers are safer using hands-free cell phones instead of using hand-held cell phones