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In: Statistics and Probability

Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before...

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 19.1 20.3 20.6 22.4 23.5 23.3 25.2 22.6 20.3

24.9 22.3 27.0 20.9 22.6 24.4 21.6 22.4 22.3 23.2

The tips for the 20 customers who received the bad-weather message are listed here:

18.0 19.3 19.4 19.1 18.4 19.5 18.7 16.3 16.8 14.3

17.0 14.1 17.8 20.2 20.7 19.2 18.0 23.3 18.7 19.8

What is the two-sample t test statistic? (Round your answer to three decimal places.)
t =

Expert Solution

Two sample t test is used to compare the mean tips between good-weather message and bad-weather message assuming equal variance.

The test is performed in following steps,

Step 1: The Null and Alternative Hypotheses

Step 2: The t statistic is used to compare the two population means and the significance level for the test is

The decision rules state the conditions that if,

,

Step 3: The t statistic is obtained using the formula,

From the samples data value,

	good-weather message	bad-weather message
Average	22.5	18.43
Std.Dev	1.9104	2.0991
n	20	20

Step 4:

The P-value for the t statistic is obtained from t distribution table for degree of freedom = n1+n2-2=20=20-2=38

The corresponding P-value is 0.0000 which is less than 0.05 at the 5% significance level for the two sided alternative hypothesis. Hence, it can be concluded that the null hypothesis is rejected. Hence we can conclude that there is significant difference in mean tips between good-weather message and bad-weather message

orchestra answered 1 year ago

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Researchers gave 40 index cards to a waitress at an Italian restaurant in New Jersey. Before...

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