Question

find the standardized test statistic t for a sample with ( n = 10 ), ( \bar{x}=13.4 ), ( s = 1.3 ), and ( alpha = 0.05 ) if ( h_{0}: mu leq 14.3 ). round your answer to three decimal places

oa. - 3.010
ob. - 3.186
oc. - 2.617
od. - 2.189

Explanation:

Step1: Recall the formula for the t - statistic

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

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

Given \(\bar{x} = 13.4\), \(\mu=14.3\), \(s = 1.3\), \(n = 10\)

Step3: Substitute the values into the formula

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Since \(\sqrt{10}\approx3.1623\), then \(t=\frac{-0.9\times3.1623}{1.3}=\frac{- 2.8461}{1.3}\approx - 2.189\)

Answer:

D. - 2.189