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, and do not assume that the population standard deviations are equal. complete parts (a) to (c).

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 $\box$. (round to two 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, and do not assume that the population standard deviations are equal. complete parts (a) to (c).

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 $\box$. (round to two decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Sample t-Test Statistic" ], "new_concepts": [], "current_concepts": [ "Two-Sample t-Test Statistic", "Hypothesis Testing for Two Means" ] } ## Calculate sample statistics for both groups $$ \begin{aligned} &\text{Regular Coke (Group 1): } n_1 = 12\ &\bar{x}_1 = \frac{0.81920 + 0.81499 + 0.81632 + 0.82107 + 0.81814 + 0.82473 + 0.80616 + 0.81277 + 0.81720 + 0.81104 + 0.82506 + 0.82640}{12} \approx 0.817757\ &s_1 \approx 0.006243\ &\text{Diet Coke (Group 2): } n_2 = 16\ &\bar{x}_2 = \frac{0.77728 + 0.77582 + 0.78957 + 0.78675 + 0.78442 + 0.78607 + 0.78059 + 0.78296 + 0.78520 + 0.78794 + 0.78812 + 0.78260 + 0.79229 + 0.78517 + 0.78717 + 0.78128}{16} \approx 0.783952\ &s_2 \approx 0.004523 \end{aligned} $$ ## Calculate the pooled standard deviation $$ \begin{aligned} &s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}\ &s_p = \sqrt{\frac{11 \times (0.006243)^2 + 15 \times (0.004523)^2}{12 + 16 - 2}} \approx 0.005315 \end{aligned} $$ ## Calculate the pooled two-sample t-test statistic $$ \begin{aligned} &t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}\ &t = \frac{0.817757 - 0.783952}{0.005315 \sqrt{\frac{1}{12} + \frac{1}{16}}} \approx \frac{0.033805}{0.005315 \times 0.381881} \approx 16.65 \end{aligned} $$ The test statistic is 16.65. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Two-Sample t-Test Statistic" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate sample statistics for both groups

Calculate the pooled standard deviation

Calculate the pooled two-sample t-test statistic

Answer: