Question

For a certain data test statistic ‘t’ is calculated as : \(|t|=|\frac{65-68}{\frac{4}{\sqrt{15}}}|=2.90\), then select the correct option :

• A. \(\bar{x}=68;\mu=65,n=16\)
• B. \(\bar{x}=65;\mu=68,n=16\)
• C. \(\bar{x}=15;n=4,\mu=3\)
• D. \(\bar{x}=65;\mu=68,n=14\)

Answer 1

The Correct Option is B

We are given that the test statistic \( |t| \) is calculated using the formula: \(|t| = \left|\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\right|\). From the given data, we know: \(|t| = 2.90\), \(\bar{x} = 65\), and \(\mu = 68\). Let's verify the calculation.

According to the formula, we have:

\(|t| = \left|\frac{65 - 68}{\frac{4}{\sqrt{15}}}\right|\)

Substituting the values:

\[|t| = \left|\frac{-3}{\frac{4}{\sqrt{15}}}\right|\]

To simplify further, calculate \(\frac{4}{\sqrt{15}}\):

\(\frac{4}{\sqrt{15}} = \frac{4 \times \sqrt{15}}{15}\)

Using this, calculate \(|t|\):

\(|t| = \left|\frac{-3 \times \sqrt{15}}{4}\right|\)

Since this expression evaluates to 2.90, the corresponding option must correctly reflect these values. The correct configuration from the options is:

\(\bar{x} = 65;\mu = 68;n = 16\)