Question

A random sample of size 9 has 21 as sample mean. The sum of the squares of the deviations taken from mean is 72. The sample is drawn from the population having 23 as mean. The value of test statistic is,

• A. -2
• B. 2
• C. -2.5
• D. -3

Answer 1

The Correct Option is A

The problem involves calculating the test statistic for a sample mean. We have the following data:

• Sample size, \( n = 9 \)
• Sample mean, \( \bar{x} = 21 \)
• Population mean, \( \mu = 23 \)
• Sum of squares of deviations from the mean, \( \sum (x - \bar{x})^2 = 72 \)

Our goal is to compute the test statistic using these steps:

1. Calculate the sample variance \( s^2 \) using the formula:
   \( s^2 = \frac{\sum (x - \bar{x})^2}{n-1} \)
   Substituting the values:
   \( s^2 = \frac{72}{9-1} = \frac{72}{8} = 9 \)
2. Calculate the sample standard deviation \( s \):
   \( s = \sqrt{9} = 3 \)
3. Compute the standard error \( SE \) of the sample mean:
   \( SE = \frac{s}{\sqrt{n}} = \frac{3}{\sqrt{9}} = \frac{3}{3} = 1 \)
4. Determine the test statistic \( t \) using the formula:
   \( t = \frac{\bar{x} - \mu}{SE} \)
   Substituting the values:
   \( t = \frac{21 - 23}{1} = \frac{-2}{1} = -2 \)

Therefore, the value of the test statistic is -2.