Question

T-Test

A research team measured 70 American men’s height. The average height of these men is 176cm and the sample variance is 16. Is the average height of American males different from 174cm?

a) State the null and alternative hypotheses

b) Compute the t-statistics

c) Draw the statistical conclusion (at 95% confidence level)

Answer 1

Solution(a)
Here claim is that average height of American males is different from 174 cm
Null hypothesis H0: mean = 174 cm
Alternative hypothesis Ha: mean is not equal to 174 cm
Solution(b)
No. of sample = 70
Sample mean = 176 cm
Sample variance = 16
Sample standard deviation = sqrt(Variance) = Sqrt(16) = 4
test statistic can be calculated as
test statistic = (Sample mean - population mean)/standard deviation/sqrt(n) = (174-176)/4/sqrt(70) = -2/(4/8.37) = -4.18
Solution(c)
No. of sample = 70
Degree of freedom = n-1 = 70-1 = 69
Confidence level = 95%
level of significance = 0.05
this is two tailed test so test critical value from t table is +/-1.99
If test stat value is less than -1.99 or greater than 1.99 than we will reject the null hypothesis else do not reject the null hypothesis.
Here we can see that test stat value is less than -1.99 i.e. (-4.18<-1.99). So we will reject the null hypothesis and we have significant evidence to say that the average height of American males different from 174 cm.