Question

Claim: fewer than 95% of adults have a cell phone. In a reputable poll of 1114 adults, 89% said that they have a cell phone. Find the value of the test statistic.

a. 2.83
b. -2.83
c. 5.15
d. Not Mentioned

Answer 1

To find the value of the test statistic, we need to use the one-proportion z-test formula. Plugging in the given values, we find that the value of the test statistic is approximately -2.83.

Step-by-step explanation:

To find the value of the test statistic, we need to use the one-proportion z-test formula. The formula is:

Z = (p - P) / √((P * (1 - P)) / n)

where p is the sample proportion (89% or 0.89), P is the hypothesized population proportion (95% or 0.95), and n is the sample size (1114).

Plugging in the values, we get:

Z = (0.89 - 0.95) / √((0.95 * (1 - 0.95)) / 1114)

Z = -0.06 / √((0.95 * 0.05) / 1114)

Z = -0.06 / √(0.0475 / 1114)

Z = -0.06 / √0.000042615

Z ≈ -2.83

Therefore, the value of the test statistic is approximately -2.83.