To apply the two-sample t procedures, use Option 1 if you have technology that i

Question

To apply the two-sample t procedures, use Option 1 if you have technology that implements that method. Otherwise, use Option 2.

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 not so good tomorrow. I hope you enjoy the day anyway!" After the customers left, the waitress recorded the amount of the tip (percent of bill) before taxes. Here are the tips for those receiving the good-weather message:

21.2   18.9   20.1   20.7   22.3   23.4   23.2   25.1   22.2   20.4

25.3   22.4   27.0   20.8   22.2   24.5   21.6   22.1   22.0   22.8

The tips for the 20 customers who received the bad-weather message are below.

18.1   19.1   19.6   18.9   18.9   19.0   18.7   16.1   17.3   14.0

17.4   14.1   17.9   20.5   20.7   19.0   18.1   23.4   18.3   19.4

Give a 95% confidence interval for the difference between the mean percent tips for the two different messages. (Round your answers to two decimal places.)

_____ to _____ percent

Explanation / Answer

X1-X2 =3.985

here degree of freedom v =((s12/n1 +s22/n2)2/((s12/n1)2/(n1-1) +(s22/n2)2/(n2-1)) =37

here std error =(s12/n1 +s22/n2)1/2 =0.6431

for 37 degree of freedom at 95% CI , t =2.026

hence confidence interval =(X1-X2) +/- t*std error =2.682 ;5.288

S. no private public 1 21.2 18.1 2 18.9 19.1 3 20.1 19.6 4 20.7 18.9 5 22.3 18.9 6 23.4 19 7 23.2 18.7 8 25.1 16.1 9 22.2 17.3 10 20.4 14 11 25.3 17.4 12 22.4 14.1 13 27 17.9 14 20.8 20.5 15 22.2 20.7 16 24.5 19 17 21.6 18.1 18 22.1 23.4 19 22 18.3 20 22.8 19.4 total 448.200 368.500 mean 22.410 18.425 std deviation(S) 1.953 2.112

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