A poll of 2,009 randomly selected adults showed that 95% of them own cell phones

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 p0.92 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, alpha.

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

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

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

Explanation / Answer

A)

ho: percentage of adults Who own cell phones is 92%. po = 0.92

V/s h1: percentage of adults who own cell phone is not 92%. po = 0.92

this is a two tailed hypothesis as the direction of alternative hypothesis is not mentioned.

B)

z = (phat-po)/sqrt(po*(1-po)/n)

here, phat = 0.95 and n = 2009

hence, z = (0.95-0.92)/sqrt(0.92*(1-0.92)/2009) = 4.9565

C)

p-value = 2*(1-P(Z<|z|) = 2*(1-P(Z<4.9565)) = 0.0000007

D)

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

Please note that in your given answers, there is mistake of X. here i am given p-hat and n.

i know that p-hat = X/n. thus X = n*phat = 2009*.95 = 1908.55 = 1909

you have mistakenly taken X as 1915. hence the difference in answers.

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