Question

a. h₀:μ₁ = μ₂
h₁:μ₁ > μ₂
c. h₀:μ₁ = μ₂
h₁:μ₁ < μ₂
d. h₀:μ₁ = μ₂
h₁:μ₁ ≠ μ₂
the test statistic, t, is -4.90. (round to two decimal places as needed.)
the p - value is 0.000. (round to three decimal places as needed.)
state the conclusion for the test.
a. reject the null hypothesis. there is not sufficient evidence to support the claim that giving candy does result in greater tips.
b. fail to reject the null hypothesis. there is sufficient evidence to support the claim that giving candy does result in greater tips.
c. reject the null hypothesis. there is suffici
d. fail to reject the null hypothesis. there is
b. construct the confidence interval suitable for t
-3.06 < μ₁ - μ₂ < -1.49
(round to two decimal places as needed.)
does the confidence interval support the conclusi
yes, because the confidence interval contains
only positive values.
only negative values.
zero.
?

Explanation:

Step1: Hypothesis Testing Rule

If the P - value is less than the significance level (commonly \( \alpha = 0.05 \)), we reject the null hypothesis. Here, the P - value is \( 0.000\) (which is less than \( 0.05\)).

Step2: Conclusion from Hypothesis Test

Since the P - value \( 0.000<0.05\), we reject the null hypothesis. When we reject the null hypothesis \(H_0:\mu_1=\mu_2\), and looking at the confidence interval \(-3.06 <\mu_1-\mu_2<-1.49\) (only negative values), it means \(\mu_1<\mu_2\) (because \(\mu_1-\mu_2<0\) implies \(\mu_1 <\mu_2\)).

Answer:

C. \(H_0:\mu_1=\mu_2\), \(H_1:\mu_1 <\mu_2\); Reject the null hypothesis. There is sufficient evidence to support the claim that giving candy does result in greater tips. Yes, because the confidence interval contains only negative values.