Question

Sixty-nine voters from a sample of 100 indicated that they favored casino gambling in their city. The city council is interested in finding out whether or not there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. Use the normal approximation to the Binomial, and conduct a two-tailed test at the .05 significance level. Suppose that favoring casino was given a "+" sign and not-favoring casino a "-" sign. What is the value of test statistic?

Select one:

A. z = 2.70

B. z = 0.37.

C. z = - 3.70

D. z = 3.70

Answer 1

Answer)

N = 100

P = 0.5 (claimed p as if both are equal then p should be 0.5)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 50

N*(1-p) = 50

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed p = 69/100 = 0.69

Claimed p = 0.5

Z = 3.8

3.7 is the closest one