Question 2, 10.3.3
HW Score: $0 %, 0$ of 9 points
Part 1 of 4
Points: 0 of 1
To test $H_{0} : μ = 40$ versus $H_{1} : μ < 40$ , a random sample of size $n = 22$ is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
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(a) If $\bar{x} = 37.5$ and $s = 13.4$ , compute the test statistic.
$t_{0} = ◻$ (Round to three decimal places as needed.)

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$- 0.875$ is the final answer.

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Step 1 ：We are given that the sample mean $\bar{x} = 37.5$ , the hypothesized population mean $μ_{0} = 40$ , the sample standard deviation $s = 13.4$ , and the sample size $n = 22$ .

Step 2 ：We are testing the hypotheses $H_{0} : μ = 40$ versus $H_{1} : μ < 40$ .

Step 3 ：The test statistic for a t-test can be calculated using the formula: $t_{0} = \frac{\bar{x} - μ_{0}}{s / \sqrt{n}}$ .

Step 4 ：Substituting the given values into the formula, we get $t_{0} = \frac{37.5 - 40}{13.4 / \sqrt{22}}$ .

Step 5 ：Solving the above expression, we find that the test statistic $t_{0} = - 0.875$ .

Step 6 ： $- 0.875$ is the final answer.

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