For a sample size of n = 100,and σ = 10,we want to test the hypothesis H0: μ = 100.The sample mean is 103.The test statistic is
A)1.645
B)1.960
C)3.000
D)0.300

Question

Quizplus · Accepted Answer

We can calculate the test statistic using the formula:

t = (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.

Plugging in the given values, we get:

t = (103 - 100) / (10 / √100) = 3

The critical value for a two-tailed test at a significance level of 0.05 with 99 degrees of freedom (n-1) is 1.984 (from a t-distribution table, or using a calculator or software).

Since our calculated test statistic (3) is greater than the critical value (1.984), we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population mean is not equal to 100. Therefore, the best choice is C.

For a Sample Size of N = 100,and σ =