Question

A random sample of 100 observations from a population with standard deviation 21.74 yielded a sample mean of 93 . Given that the null hypothesis isμ=90 and the alternative hypothesis is μ>90 using α=.05, find the Test statistic =

Answer 1

To find the test statistic in a hypothesis test with a known sample mean and standard deviation, use the formula (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Given the sample mean, population mean, sample standard deviation, and sample size, we can calculate the test statistic to be 1.38.

Step-by-step explanation:

To find the test statistic in a hypothesis test, we need to calculate the z-score or t-score, depending on whether we know the population standard deviation or not. In this case, we do not know the population standard deviation, so we will use the t-distribution.

To calculate the test statistic, we can use the formula:

Test statistic = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Given that the sample mean is 93, the population mean is 90, the sample standard deviation is 21.74, and the sample size is 100, we can plug in these values to calculate the test statistic.

Test statistic = (93 - 90) / (21.74 / sqrt(100)) = 3 / (21.74 / 10) = 3 / 2.174 = 1.38