Question

Monster energy drink is supposed to have a 16 ounces size. In this test there was six monster drinks tested and the average amount in each can was 13.22 ounces. The standard deviation is 2.05. (Use significance level .01)

(1) Calculate confidence interval

(2) Find test-statistic

(3) Find p-value

(4) Reject null or do not reject null

Answer 1

To Test :-

H0 :- $\mu = 16$

H1 :- $\mu \neq 16$

Part a)

Confidence Interval
$\bar{X} \pm t_{\alpha /2, n-1} S/\sqrt{n}$
$t_{\alpha /2, n-1} = t_{ 0.01 /2, 6- 1 } = 4.032$
$13.22 \pm t_{\ 0.01/2, 6 -1} * 2.05/\sqrt{ 6}$
Lower Limit = $13.22 - t_{\ 0.01/2, 6 -1}2.05/\sqrt{ 6}$
Lower Limit = 9.8455
Upper Limit = $13.22 + t_{\ 0.01/2, 6 -1}2.05/\sqrt{ 6}$
Upper Limit = 16.5945
99% Confidence interval is ( 9.8455 , 16.5945 )

Part 2)

Test Statistic :-
$t = ( \bar{X} - \mu ) / (S /\sqrt{n})$
$t = ( 13.22 - 16 ) / ( 2.05 /\sqrt{ 6 })$
t = -3.3217

Part 3)

P value = 2 * P ( t > 3.3217 ) = 0.0210

Part 4)

Reject null hypothesis if P value < $\alpha = 0.01$ level of significance

P value = 0.0210 > 0.01, hence we fail to reject null hypothesis

Conclusion :- Do not reject null