Question

assume that a simple random sample has been selected from a normally distributed population. find the test statistic t.
a local newspaper reported that for the adult population of a town, the mean annual salary is $30,000. test the claim that for the adult population of this town, the mean annual salary is greater than $30,000. sample data are summarized as n = 17, sample mean = $22,298, and s = $14,200. use a significance level of alpha = 0.05. find the test statistic t.
-2.24
-1.57
1.57
2.24
0.05

Explanation:

Step1: Recall the formula for the t - test statistic

The formula for the one - sample t - test statistic is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the hypothesized population mean, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Step2: Identify the values from the problem

We are given that \(\bar{x} = 22298\), \(\mu=30000\), \(s = 14200\), and \(n = 17\).

Step3: Substitute the values into the formula

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Answer:

-2.24