Question

In a random sample of 43 teenage males it was found that the amount of soda they consumed daily had a mean of 33.42 ounces with a standard deviation of 9.98 ounces. At the 1% level of significance can it be shown that teenage males consume a mean of less than 36 ounces of soda per day?

(a) State and test appropriate hypotheses. State conclusions.

(b) Find the p-value of the test in (a).

Answer 1

Here we have to test that

Null hypothesis :

Alternative hypothesis :

where

n = sample size = 43

Sample mean = 33.42

Sample standard deviation = s = 9.98

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

Test statistic :

t = -1.695 (Round to 3 decimal)

Test statistic = -1.695

Level of significance = = 0.01

Test is left tailed test.

Degrees of freedom = n - 1 = 43 - 1 = 42

t critical value for = 0.01 and df = 42 from excel using function:

=T.INV(0.01,42)

=-2.418

t criticl value = -2.418

Here test statistic > t critical value.

So we fail to reject H0

Conclusion : There is insufficient evidence to show that teenage males consume a mean of less than 36 ounces of soda per day

b)

P value from excel usinf function:

=T.DIST(-1.695, 42, TRUE)

= 0.0487 (Round to 4 decimal

P value = 0.0487

Here p value >

So we fail to reject H0.

Conclusion : There is insufficient evidence to show that teenage males consume a mean of less than 36 ounces of soda per day