Question

People tend to be more generous after receiving good news. Are they less generous after receiving bad news? The average tip left by adult Americans is 21%. Give 20 patrons of a restaurant a message on their bill warning them that tomorrow's weather will be bad and record the percentage tip they leave. Given are the tips as a percentage of the total bil. 18 19.119.2 18.8 18.4 19 18.5 16.1 16.8 18.2 14 1713.6 17.5 20 20.2 18.818 23.2 19.4 Suppose that percentage tips are Normal with ơ 1.8 . To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV Crunchlt! STATE: Is there good evidence that the mean percentage tip is less than 21% ? PLAN: Let μ be the average tip percentage for all customers receiving bad news. Choose the correct hypotheses to test. 0 H 0: μ 21 versus Ha: μ > 21 H0: μ = 21 versus Ha: μチ21 O Ho: μ = 21 versus Ha: μ < 21 0 H0: μ < 21 versus Ha: μ > 21

Answer 1

H₀: $\mu$ = 21

H_a: $\mu$ < 21

$\bar x$ = (18 + 19.1 + 19.2 + 18.8 + 18.4 + 19 + 18.5 + 16.1 + 16.8 + 18.2 + 14 + 17 + 13.6 + 17.5 + 20 + 20.2 + 18.8 + 18 + 23.2 + 19.4)/20 = 18.19

z = ($\bar x - \mu$)/($\sigma/\sqrt n$)

   = (18.19 - 21)/(1.8/)

V20

   = -6.98

P-value = P(Z < -6.98)

             = 0.000

At the 0.05 significance level, since the P-value is less than the significance level(0 < 0.05), so we should reject H₀.

Option - D) There is sufficient evidence that the average tip percentage , when bad news is delivered , is lower than the average tip percentage overall. Random chance explains the small value of $\bar x$ observed.