This Question: 8 pts 412 of 25 (0 complete)> This Test: 100 pts possible A resea

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This Question: 8 pts 412 of 25 (0 complete)> This Test: 100 pts possible A research center clims that at most 75% of adults in a certain country think that drivers are sater using hands-free cell phones instead of using hand-held cell phones in a random sample of 150 adults from hat country, 78% think that drivers are safer using hands-free cell phones instead of using hand-held cell phones. At ?-0.01, is there enough evidence to re ect the center's daim? Complete parts a through e below. (a) Identify the caim and state Ho and Ha What is the claim? o A. ( B. ° ?. 0 D. Exactly 78% of adults in the country think that drivers are safer using hands-free cell phones instead of using hand-held cell phones. At most 75% of adults in the country think that drivers are safer using hands-free cell phones instead of using hand-held cell phones At most 75% of all adults think that drivers are safer using hands-free cell phones instead of using hand-held cell phones. Exactly 78% of all adults think that drivers are safer using hands-free cell phones instead of using hand-held cell phones. Identify Ho and Ha (Type integers or decimals.) (b) Find the critical value(s) and identify the rejection region(s) The critical value(e) is'are zo (Round to two decimal places as needed. Use a comma to separate answers as needed.) What is/are the rejection region(s)? Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.) z

Explanation / Answer

Solution:-

a) B) Atmost 75% of the adults in the country thinks that the drivers are safer using hand free cell phones instead of using hand held cell phones.

b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.75
Alternative hypothesis: P > 0.75

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.03536
z = (p - P) / S.D

z = 0.848

zcritical = 2.327

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is more than 0.848.

Thus, the P-value = 0.198.

Interpret results. Since the P-value (0.198) is more than the significance level (0.01), we have to accept the null hypothesis.

Do not reject H0, There is enough evidence at the 1% level of significance to accept the center's claim that atmost 75% of adults think that drivers are safer using hands free cell phones instead of using hand held cell phones.

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