Question

When birth weights were recorded for a simple random sample of 16 male babies born to mothers taking a special vitamin supplement, the sample had a mean of 3.675 kilograms and a standard deviation of 0.657 kilogram. The birth weights for all babies are assumed to normally distributed. Use a 0.05 significance level to test the claim that the mean birth weight for all male babies of mothers taking the vitamin supplement is different from 3.39 kilograms, which is the mean for the population of all males.

a. What are the null and alternative hypotheses?

b. Is this a left-tailed, right-tailed or two-tailed test?

c. What is the t-score for this sample mean?

d. What is the critical value of t for this test?

e. State the conclusion

Answer 1

Solution:

a)

The null and alternative hypothesis is,

Ho: 3.39

Ha: 3.39

b)

This is a two tailed test.

c)

The test statistics,

t =( - )/ (s /n)

= ( 3.675 - 3.39 ) / ( 0.657 / 16 )

= 1.735

d)

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 2.131

Since it is observed that t = 1.735 < = 2.131, it is then concluded that fail to reject the null hypothesis.

There is not sufficient evidence to claim that the mean birth weight for all male babies of mothers taking the vitamin supplement is different from 3.39 kilograms