Data on the weights​ (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal.

Diet  Regular
u u1 u2
n 36 36
x overbar 0.78616 lb 0.81111 lb
s 0.00444 lb 0.00752 lb 

a. The test​ statistic, t:________
b. P-Value: ________
c. Conclusion of test
d. Construct a confidence interveral appropriate for the hypothesis test.
e. Does the confidence interval support conclusion of hypothesis test?

Answer:

Test = 17.143 ;

Pvalue = 0 ;

Reject the Null ;

(-0.028 ; - 0.022) ;

We conclude that content are different.

Step-by-step explanation:

Given that:

μ1 = μ

n1 = 36 ; n2 = 36

x1 = 0.78616 ; x2 = 0.81111

s1 = 0.04444 ; s2 = 0.00752

Test statistic :

(x1 - x2) / √(s1²/n1 + s2²/n2)

(0.78616 - 0.81111) / √(0.00444²/36 + 0.00752²/36)

- 0.02495 / 0.0014554

= 17.143

Pvalue :

Z < 17.143

Pvalue = 0

Since Pvalue < α ; Reject the Null

The confidence interval using a confidence interval calculator is (-0.028 ; - 0.022)

Since the interval does not contain Zero ; then we reject the Null and conclude that the content are different.

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