an experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. the mean tip percentages and standard deviations are given in the accompanying table along with the sample sizes. assume that the 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) and (b). \begin{tabular}{|l|c|c|c|c|} \hline & \mu & n & \bar{x} & s \\ \hline no candy & \mu_1 & 40 & 18.94 & 1.31 \\ \hline two candles & \mu_2 & 40 & 21.67 & 2.48 \\ \hline \end{tabular} a. use a 0.01 significance level to test the claim that giving candy does result in greater tips. what are the null and alternative hypotheses? a. $h_0: \mu_1 \ eq \mu_2$ $h_1: \mu_1

Question

an experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. the mean tip percentages and standard deviations are given in the accompanying table along with the sample sizes. assume that the 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) and (b).

\begin{tabular}{|l|c|c|c|c|}
\hline
& \mu & n & \bar{x} & s \\
\hline
no candy & \mu_1 & 40 & 18.94 & 1.31 \\
\hline
two candles & \mu_2 & 40 & 21.67 & 2.48 \\
\hline
\end{tabular}

a. use a 0.01 significance level to test the claim that giving candy does result in greater tips.

what are the null and alternative hypotheses?

a. $h_0: \mu_1 \
eq \mu_2$
$h_1: \mu_1 < \mu_2$

b. $h_0: \mu_1 = \mu_2$
$h_1: \mu_1 \
eq \mu_2$

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

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

the test statistic, t, is -6.16. (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. fail to reject the null hypothesis. there is not sufficient evidence to support the claim that giving candy does result in greater tips.
b. reject the null hypothesis. there is sufficient evidence to support the claim that giving candy does result in greater tips.
c. fail to reject the null hypothesis. there is sufficient evidence to support the claim that giving candy does result in greater tips.
d. reject the null hypothesis. there is not sufficient evidence to support the claim that giving candy does result in greater tips.

b. construct the confidence interval suitable for testing the claim in part (a).

$-3.81 < \mu_1 - \mu_2 < -1.65$
(round to two decimal places as needed.)

does the confidence interval support the conclusion found with the hypothesis test?

no, because the confidence interval contains only negative values

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Two-Sample t-Test Statistic" ], "current_concepts": [ "Two-Sample t-Test Statistic", "Hypothesis Testing for Two Means" ] } ## Identify given values and formula $$ \begin{aligned} &\text{No candy (Group 1): } n_1 = 40, \bar{x}_1 = 18.94, s_1 = 1.31 \ &\text{Two candles (Group 2): } n_2 = 40, \bar{x}_2 = 21.67, s_2 = 2.48 \ &t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \quad (\text{where } \mu_1 - \mu_2 = 0) \end{aligned} $$ ## Calculate test statistic $$ \begin{aligned} &t = \frac{18.94 - 21.67}{\sqrt{\frac{1.31^2}{40} + \frac{2.48^2}{40}}} \ &t = \frac{-2.73}{\sqrt{\frac{1.7161}{40} + \frac{6.1504}{40}}} \ &t = \frac{-2.73}{\sqrt{0.0429025 + 0.15376}} \ &t = \frac{-2.73}{\sqrt{0.1966625}} \ &t \approx \frac{-2.73}{0.443466} \approx -6.156 \end{aligned} $$ ## Round to two decimal places $$ t \approx -6.16 $$ The test statistic, t, is $-6.16$ (Round to two decimal places as needed.) { "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:

Identify given values and formula

Calculate test statistic

Round to two decimal places

Answer: