In testing the hypotheses H₀: μ = 50 vs.H₁: μ ≠ 50,the following information is known: n = 64, = 53.5,and σ = 10.The standardized test statistic z equals: A)1.96 B)−2.80 C)2.80 D)−1.96

Question

Quizplus · Accepted Answer

We can calculate the standardized test statistic (z-score) using the formula:

z = (x̄ - μ) / (σ / √n)

where x̄ is the sample mean, μ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (53.5 - 50) / (10 / √64)
z = 3.5 / 1.25
z = 2.80

Since the alternative hypothesis is μ ≠ 50 (two-tailed test), we need to calculate the critical value of z at the 5% significance level, which is ±1.96 (obtained from a standard normal distribution table or calculator).

Since our calculated z-score of 2.80 is greater than the critical value of 1.96, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the population mean is not equal to 50.

Therefore, the correct answer is C.

In Testing the Hypotheses H0: μ = 50 Vs

In Testing the Hypotheses H₀: μ = 50 Vs