Question

find the standardized test statistic t for a sample with ( n = 15 ), ( overline{x} = 6.2 ), ( s = 0.8 ), and ( alpha = 0.05 ) if ( h_{0}: mu leq 5.9 ). round your answer to two decimal places.

a. 1.63
b. 1.73
c. 1.31
d. 1.45

Explanation:

Step1: Recall the formula for the t - statistic

The formula for the t - statistic in a one - sample t - test is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\)

Step2: Identify the values of \(\bar{x}\), \(\mu\), \(s\) and \(n\)

Given \(\bar{x} = 6.2\), \(\mu = 5.9\) (from \(H_0:\mu\leq5.9\)), \(s = 0.8\), \(n=15\)

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Since \(\sqrt{15}\approx3.87298\), then \(0.3\times\sqrt{15}\approx0.3\times3.87298 = 1.16189\)

$$t=\frac{1.16189}{0.8}=1.45236\approx1.45$$

Answer:

D. 1.45