Question

A poll of 2,009 randomly selected adults showed that 95% of them own cell phones. The technology display below results from a test of the claim that 92​% of adults own cell phones. Use the normal distribution as an approximation to the binomial​ distribution, and assume a 0.05 significance level to complete parts​ (a) through​(e). Test of p=0.920.92 vs p≠0.92 Sample=1, X=1915 N=2,009, Sample p=.953211, 95%CI (.943976, .962445), ​Z-Value=5.49​P-Value=0.000
Is the test​ two-tailed, left-tailed, or​ right-tailed?

What is the test​ statistic?

What is the​ P-value?

What is the null hypothesis and what do you conclude about​it?

Choose the correct answer below.

A. Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alphaα.

B. Fail to rejectFail to reject the null hypothesis because the​P-value is greater than the significance​ level, alphaα.

C.Fail to rejectFail to reject the null hypothesis because the​P-value is less than or equal to the significance​ level, alphaα.

D.Reject the null hypothesis because the​ P-value is greater than the significance​ level, alphaα.

Answer 1

Answer:

a) two-tailed test

b) Z=5.49

c) P-value=0.000

d) The null hypothesis states that the proportion is equal to 0.92 (p=0.92).

As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected.

e) A. Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level α.

Step-by-step explanation:

a) Is the test​ two-tailed, left-tailed, or​ right-tailed?

As the alternative hypothesis is defined with a unequal sign, the rejection can happen for a sample statistic that is too low or too high. So both tails are part of the rejection region. Then, this test is a two-tailed test.

b) What is the test​ statistic?

The test statistic is the Z-value: Z=5.49.

c) What is the​ P-value?

The P-value is P=0.000, corresponding to the Z-value of point b.

d) What is the null hypothesis and what do you conclude about​ it?

The null hypothesis states that the proportion is equal to 0.92 (p=0.92).

As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected.

e) As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected.

A. Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level α.