Question

A new gym just opened up in North Van. Jon V the owner, needs to calculate the amount of space required for parking. According to his research, 50% of staff and gym users use public transportation. A survey of 1002 was conducted, and 483 responded that they used public transportation. Is it reasonable to conclude that the survey results indicate a change? Use the 0.05 significance level. Compute the value of the test statistic. Hint. The test statistic is the value obtained in step 5 of hypothesis testing. Select one: O

a.-2.33
b.-3.33
c.-1.14
d. 0.025
e. 0.05
f. -1.96
g. 6.45
h. 3.33

Answer 1

Using hypothesis testing at the 0.05 significance level, a z-test statistic was calculated to determine if there is a significant change in the use of public transportation among gym users and staff. The test statistic was found to be approximately -1.96.

Step-by-step explanation:

To determine if there is a significant change in the number of gym users and staff that use public transportation, we conduct hypothesis testing using the 0.05 significance level. Let's define our null hypothesis (H0) as the proportion of public transportation users being 50%, and the alternative hypothesis (Ha) as it being different from 50%.

The formula to calculate the test statistic in a proportion hypothesis test is:

z = (p - P0) / sqrt(P0(1-P0)/n)

where:

• p is the sample proportion
• P0 is the hypothesized population proportion
• n is the sample size

In this case, p = 483/1002, P0 = 0.50, and n = 1002.

Calculating the test statistic:

z = (483/1002 - 0.50) / sqrt(0.50 * 0.50 / 1002)

z ≈ -1.96

Since -1.96 is the value of the test statistic, the correct answer is f. -1.96.