Question

A sample of 10 measurements, randomly selected from a normally distributed population, resulted in a sample mean=5.2, and sample standard deviation=1.8. Using ,alpha=0.01 test the null hypothesis that the mean of the population is 3.3 against the alternative hypothesis that the mean of the population < 3.3, by giving the following:

degrees of freedom =9

critical t value

the test statistic

Answer 1

Here we have to test that

Null hypothesis :

Alternative hypothesis :

where

n = sample size = 10

Sample mean = = 5.2

Sample standard deviation = s = 1.8

Here population standard deviation is not known so we use t test.

Test statistic :

t = 3.338 (Round to 3 decimal)

Test statistic = t = 3.338

Critical value :

Level of significance = = 0.01

Degrees of freedom = n - 1 = 10 - 1 = 9

t critical value for = 0.01 and df = 9 is

tc = 2.821 (From statistical table of t values)

As test is left tailed test, tc = -2.821 (Due to symmetry)

Critical value = -2.821

Here test statistic > critical value

So we fail to reject the null hypothesis.

Conclusion : There is not sufficient evidence to conclude that the mean of the population is less than 3.3