listed in the accompanying table are weights (lb) of samples of the contents of cans of regular coke and diet coke. assume that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. complete parts (a) to (c).

click the icon to view the data table of can weights.

a. use a 0.01 significance level to test the claim that the contents of cans of regular coke have weights with a mean that is greater than the mean for diet coke.

what are the null and alternative hypotheses? assume that population 1 consists of regular coke and population 2 consists of diet coke.

a. \$h_0: \mu_1 \le \mu_2\$
\$h_1: \mu_1 > \mu_2\$

b. \$h_0: \mu_1 \
e \mu_2\$
\$h_1: \mu_1 > \mu_2\$

c. \$h_0: \mu_1 = \mu_2\$
\$h_1: \mu_1 > \mu_2\$

d. \$h_0: \mu_1 = \mu_2\$
\$h_1: \mu_1 \
e \mu_2\$

the test statistic is 16.65. (round to two decimal places as needed.)

the p-value is 0. (round to three decimal places as needed.)

state the conclusion for the test.

a. reject the null hypothesis. there is sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.
b. fail to reject the null hypothesis. there is sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.
c. reject the null hypothesis. there is not sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.
d. fail to reject the null hypothesis. there is not sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.

b. construct the confidence interval appropriate for the hypothesis test in part (a).

\$0.029 < \mu_1 - \mu_2 < 0.035\$
(round to three decimal places as needed.)

Question

listed in the accompanying table are weights (lb) of samples of the contents of cans of regular coke and diet coke. assume that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. complete parts (a) to (c).

click the icon to view the data table of can weights.

a. use a 0.01 significance level to test the claim that the contents of cans of regular coke have weights with a mean that is greater than the mean for diet coke.

what are the null and alternative hypotheses? assume that population 1 consists of regular coke and population 2 consists of diet coke.

a. \$h_0: \mu_1 \le \mu_2\$
\$h_1: \mu_1 > \mu_2\$

b. \$h_0: \mu_1 \
e \mu_2\$
\$h_1: \mu_1 > \mu_2\$

c. \$h_0: \mu_1 = \mu_2\$
\$h_1: \mu_1 > \mu_2\$

d. \$h_0: \mu_1 = \mu_2\$
\$h_1: \mu_1 \
e \mu_2\$

the test statistic is 16.65. (round to two decimal places as needed.)

the p-value is 0. (round to three decimal places as needed.)

state the conclusion for the test.

a. reject the null hypothesis. there is sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.
b. fail to reject the null hypothesis. there is sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.
c. reject the null hypothesis. there is not sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.
d. fail to reject the null hypothesis. there is not sufficient evidence to support the claim that cans of regular coke have weights with a mean that is greater than the mean for diet coke.

b. construct the confidence interval appropriate for the hypothesis test in part (a).

\$0.029 < \mu_1 - \mu_2 < 0.035\$
(round to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Sample t-Test Statistic" ], "new_concepts": [], "current_concepts": [ "Two-Sample t-Test Statistic", "Two-Sample Confidence Interval" ] } ## Calculate sample statistics for both groups $$ \begin{aligned} &\text{Regular Coke (Group 1): } n_1 = 12\ &\bar{x}_1 \approx 0.81682,\quad s_1 \approx 0.00751\ &\text{Diet Coke (Group 2): } n_2 = 12\ &\bar{x}_2 \approx 0.78479,\quad s_2 \approx 0.00439 \end{aligned} $$ ## Compute the two-sample t-test statistic $$ \begin{aligned} &t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\ &t = \frac{0.81682 - 0.78479}{\sqrt{\frac{0.00751^2}{12} + \frac{0.00439^2}{12}}} \approx 16.65 \end{aligned} $$ $t = 16.65$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Statistics", "Two-Sample t-Test Statistic" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate sample statistics for both groups

Compute the two-sample t-test statistic

Answer: