Question

1. Claim Fewer than 97 % of adults have a cell phone. In a reputable poll of 1038 adults, 89 % said that they have a cell phone. Find the value of the test statistic.

2. The test statistic of z=1.38 is obtained when testing the claim that p>0.2

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value by the calculator or by the table.

c. Using a significance level of α=0.05 should we reject H₀ or should we fail to reject H₀

Answer 1

Question 1:
The test statistic here is computed as:

$z = \frac{p-P}{\sqrt{\frac{P(1-P)}{n}}} = \frac{0.89- 0.97}{\sqrt{\frac{0.97*0.03}{1038}}} = -15.1092$

Therefore -15.1092 is the required test statistic value here.

Question 2:

a) As we are testing here whether p > 0.2 which is that we are testing it from upper side only, therefore this is a right tailed test.

b) The p-value here is computed from the standard normal tables as:

p = P(Z > 1.38 ) = 0.0838

Therefore 0.0838 is the required p-value here.

c) As the p-value here is 0.0838 > 0.05, therefore the test is not significant, and we cannot reject the null hypothesis here.