Question

Psychologists studied the size of the tip in a restaurant when a message indicating that the next day's weather would be good was written on the bill. Data below gives info on the tips for 20 patrons, measured in percent of the total bill. Past experience with patrons of the restaurant indicate a stdev sigma = 2. Construct and Interpret a 95% confidence interval for the mean percentage tip for all patrons of this restaurant when they receive a message on their bill indicating that the next day's weather will be good. tip%s 20.8 24.9 18.7 22.3 19.9 27.0 20.6 20.4 21.9 22.2 23.4 24.0 22.8 21.1 24.9 22.1 22.2 22.0 20.3 22.7

Answer #1

Sample size = n = 20

Sample mean = = 22.21

Population standard deviation = = 2

We have to construct 95% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.96 ( Using z table)

So confidence interval is ( 22.21 - 0.876539 , 22.21 + 0.876539)
= > **( 21.3335 , 23.0865)**

Interpretation: We are 95% confidence that population mean lies into given interval.

*Please Show Work*
Researchers gave 40 index cards to a waitress at an Italian
restaurant in New Jersey. Before delivering the bill to each
customer, the waitress randomly selected a card and wrote on the
bill the same message that was printed on the index card. Twenty of
the cards had the message "The weather is supposed to be really
good tomorrow. I hope you enjoy the day!" Another 20 cards
contained the message "The weather is supposed to be...

Problem #1 Confidence Interval for Means using the t and
z Distribution. Psychologists studied
the percent tip at a restaurant when a message indicating that the
next day’s weather would be nice was written on the bill. Here are
tips from a random sample of patrons who received such a bill,
measured in percent of the total bill:
20.8 18.7
19.9 20.6
21.9 23.4
22.8 24.9
22.2 20.3
24.9 22.3
27.0 20.4
22.2 24.0
21.1 22.1
22.0 22.7
Open an...

QUESTION 1:
Researchers gave 20 index cards to a waitress at an Italian
restaurant in New Jersey. Before delivering the bill to each
customer, the waitress randomly selected a card and wrote on the
bill the same message that was printed on the index card. 20 of the
cards had the message "The weather is supposed to be really good
tomorrow. I hope you enjoy the day!" Another 20 cards contained the
message "The weather is supposed to be not...

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