Question

researcher wants to show that fewer than 40% of the population exercise regularly. he samples 900 individuals and 342 of them exercise regularly. what is the value of the test statistic? a. z

Answer 1

The value of the test statistic for the one-sample z-test for proportions, based on the given sample proportions, is z = -1.22.

Step-by-step explanation:

To calculate the test statistic for the given problem, where the researcher wants to prove that fewer than 40% of the population exercise regularly, we can use the formula for a one-sample z-test for proportions. The formula for the test statistic (z) is:

z = (p - p₀)/√(p₀(1 - p₀)/n)

where:

• p is the sample proportion,
• p₀ is the null hypothesis proportion,
• n is the sample size.

In this case:

• p = 342/900 = 0.38,
• p₀ = 0.40,
• n = 900.

Plugging these values into the formula, we get:

z = (0.38 - 0.40)/√(0.40×0.60/900)

z = -0.02/√(0.40×0.60/900)

z = -0.02/0.01633

z = -1.22

Therefore, the value of the test statistic is z = -1.22.