Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80.The sample size is 49 and alpha =.05.If the sample mean is 84 and the population standard deviation is 14, the observed z value is ___.
A)2
B)-2
C)14
D)-14
E)49

Question

Quizplus · Accepted Answer

We can use the formula for the test statistic:
z = (x̄ - μ) / (σ/√n)
where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the given values, we get:
z = (84 - 80) / (14/√49)
z = 4 / 2
z = 2
Since we are testing the alternative hypothesis that the population mean is greater than 80, we are interested in the right tail of the normal distribution. Using a significance level of .05, the critical z-value is 1.645 (found using a z-table or a calculator). Since the observed z-value of 2 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population mean is greater than 80.

Suppose You Are Testing the Null Hypothesis That a Population