A simple random sample of size n = 200 drivers were asked if they drive a car ma

Question

A simple random sample of size n = 200 drivers were asked if they drive a car manufactured in a certain country. Of the 200 drivers surveyed, 110 responded that they did. Determine if more than half of all drivers drive a car made in this country at the a = 0.05 level of significance. Complete parts (a) through (d). (a) Determine the null and alternative hypotheses. H_0: 0.5 H_1: 0.5 (b) Calculate the P-value. P-value = (Round to three decimal places as needed.) (c) State the conclusion for the test. Choose the correct answer below. A. Do not reject H_0 because the P-value is greater than the alpha = 0.05 level of significance. B. Do not reject H_0 because the P-value is less than the alpha = 0.05 level of significance. C. Reject H_0 because the P-value is greater than the alpha = 0.05 level of significance. D. Reject H_0 because the P-value is less than the alpha = 0.05 level of significance. (d) State the conclusion in context of the problem. There sufficient evidence at the alpha = 0.05 level of significance to conclude that more than half of all drivers drive a car made in this country.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:

Hence,

a) H0 : p = 0.5
HA : p > 0.5

b) P-value = 0.079

c) Option D

d) is

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 110 200 0.55 0.035355339 1.4142136 0.0786

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