Question

A survey of 64 medical labs revealed that the mean price charged for certain test was Rs 120 with standard deviation of Rs 60.Test whether the data indicates that the mean price of this the test is more than Rs 100 at 5% level of significance.

Answer 1

first, we have to calculate t - test statistic , use formula $t=\frac{\bar{x}-\mu_0}{\frac{s}{\sqrt{n}}}$

where t is the test statistic and has n -1 degrees of freedom.
$\bar{x}$ is the sample mean,
$\mu_0$ is the population mean under the null hypothesis.
s is the sample standard deviation.
n is the same size.

here, $\bar{x}$ = 120 , $\mu_0$ = 100, s = 60 and n = 64

so, t = (120 - 100)/{60/√64} = 20/(60/8) = 160/60 = 2.67

now, we have to test whether the data indicates that the mean price of this the test is more than Rs 100 at 5% level of significance.
so, the critical value at 5% significance is only 1.64.