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 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) and (b).

\
$\begin{tabular}{|c|c|c|c|c|} \\hline & \\mu & n & \\bar{x} & s \\\\ \\hline \\text{no candy} & \\mu_1 & 40 & 18.94 & 1.31 \\\\ \\hline \\text{two candies} & \\mu_2 & 40 & 21.67 & 2.48 \\\\ \\hline \\end{tabular}$
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 \square (round to two decimal places as needed.)

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 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) and (b).

\begin{tabular}{|c|c|c|c|c|}
\hline
& \mu & n & \bar{x} & s \\
\hline
\text{no candy} & \mu_1 & 40 & 18.94 & 1.31 \\
\hline
\text{two candies} & \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 \square (round to two decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Null and Alternative Hypotheses", "Two-Sample t-Test" ], "new_concepts": [], "current_concepts": [ "Null and Alternative Hypotheses", "Two-Sample t-Test", "Hypothesis Testing for Two Means" ] } ## Identify the given sample statistics $$ \begin{aligned} &\text{Group 1 (No candy): } n_1 = 40, \bar{x}_1 = 18.94, s_1 = 1.31\ &\text{Group 2 (Two candies): } n_2 = 40, \bar{x}_2 = 21.67, s_2 = 2.48 \end{aligned} $$ ## State the null and alternative hypotheses $$ \begin{aligned} &H_0: \mu_1 = \mu_2\ &H_1: \mu_1 < \mu_2 \end{aligned} $$ ## Calculate the two-sample t-test statistic $$ \begin{aligned} t &= \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\ t &= \frac{18.94 - 21.67}{\sqrt{\frac{1.31^2}{40} + \frac{2.48^2}{40}}}\ t &= \frac{-2.73}{\sqrt{\frac{1.7161}{40} + \frac{6.1504}{40}}}\ t &= \frac{-2.73}{\sqrt{0.0429025 + 0.15376}}\ t &= \frac{-2.73}{\sqrt{0.1966625}}\ t &\approx \frac{-2.73}{0.443466}\ t &\approx -6.156 \approx -6.16 \end{aligned} $$ ## Question 1 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. $H_0: \mu_1 = \mu_2$, $H_1: \mu_1 > \mu_2$ ## Question 2 The test statistic, t, is -6.16 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Two-Sample t-Test" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given sample statistics

State the null and alternative hypotheses

Calculate the two-sample t-test statistic

Answer:

Question 1

Question 2