Question

A school authority claims that the average height of students is 178 cm. A researcher has taken a well-designed survey and his sample mean is 177.5 cm and the sample standard deviation is 2. The sample size is 25. 

Which statement is correct? 

a.) The result of the survey is statistically significant. 

b.) The sample mean and population mean is the same. 

c.) The result of the survey is biased. 

d.) The difference exists due to chance since the test statistic is small 

Answer 1

Hypothesis:

\(H_{0}: \mu=178\)

\(H_{1}: \mu \neq 178\)

Test statistic,

\(t=\frac{\bar{X}-\mu_{0}}{s / \sqrt{n}}\)

\(t=\frac{177.5-178}{2 / \sqrt{25}}\)

\(t=-1.25\)

Degrees of freedom for this test \(=\mathrm{n}-1=25-1=24\)

Critical value at \(5 \%\) level of significance \(=2.064\)

Since absolute value of test statistic is less than critical value we fail to raject null hypothesis at \(5 \%\) level of significance.

Hence we conclude that the difference exists due to chance since the test statistic is small.