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 20%20% . Give 2020 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 bill.

1818	19.119.1	19.219.2	18.818.8	18.418.4	1919	18.518.5	16.116.1	16.816.8	18.218.2
1414	1717	13.613.6	17.517.5	2020	20.220.2	18.818.8	1818	23.223.2	19.419.4

Suppose that percentage tips are Normal with ?=1.7σ=1.7 .

STATE: Is there good evidence that the mean percentage tip is less than 20%20% ?

PLAN: Let ?μ be the average tip percentage for all customers receiving bad news. Choose the correct hypotheses to test.

?0:?=20H0:μ=20 versus ??:?<20Ha:μ<20

?0:?<20H0:μ<20 versus ??:?>20Ha:μ>20

?0:?=20H0:μ=20 versus ??:?≠20Ha:μ≠20

?0:?≠20H0:μ≠20 versus ??:?>20Ha:μ>20

SOLVE: We have a random sample of ?=20n=20 customers and were told to assume tips have a Normal distribution. Find ?¯x¯ . (Enter your answer rounded to two decimal places.)

?¯=

Find the ?z statistic. (Enter your answer rounded to two decimal places.)

?=

Using the software of your choice or Table A, find the ?P‑value. (Enter your answer rounded to three decimal places.)

?‑value=

CONCLUDE: What conclusion can you make?

There is insufficient evidence that the average tip percentage, when bad news is delivered, is higher than the average tip percentage overall. Random chance does not explain the small value of ?¯x¯ observed.

There is sufficient evidence that the average tip percentage, when bad news is delivered, is lower than the average tip percentage overall. Random chance does not explain the small value of ?¯x¯ observed.

There is insufficient 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 ?¯x¯ observed.

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 ?¯x¯ observed.

Answer 1

the given data are:-

sample size (n) = 20

population sd () = 1.7

a),hypothesis:-

[ claim ]

b).the test statistic be:-

c).the p value is :-

[ in any blank cell of excel type =NORMSDIST(-4.76) ]

d).p value = 0.000 < 0.01 (alpha)

we reject the null hypothesis.

There is sufficient evidence that the average tip percentage, when bad news is delivered, is lower than the average tip percentage overall. Random chance does not explain the small value of observed.

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