Question

In: Statistics and Probability

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here is the data:

19.68, 14.22, 15.42, 11.6,   27.45,   18.44, 20.77,   16.74.
He wishes to test the null hypothesis that the average amount of money people have in their pockets is equal to $20. Calculate the test statistic to two decimal places. Take all calculations toward the answer to three decimal places.

Solutions

Expert Solution

Solution:|
Given in the question
Null hypothesis H0: = 20
Alternate hypothesis Ha: 20
n=8
First we will calculate Sample mean and standard deviation which can be calculated as
Sample mean (Xbar)= Xi/n = (19.68 + 14.22 + 15.42 + 11.6 + 27.45 + 18.44 + 20.77 + 16.74)/8 = 144.32/8 = 18.04
Sample standard deviation(S) = sqrt(((Xi-mean)^2/(n-1)) = sqrt((19.68-18.04)^2 + (14.22-18.04)^2 + (15.42-18.04)^2 + (11.6-18.04)^2 + (27.45-18.04)^2 + (18.44-18.04)^2 + (20.77-18.04)^2 + (16.74-18.04)^2)/7)) = sqrt(163.471/7) = 4.832
Here we will use t test as sample size is small and population standard deviation is unknown so test stat value can be calculated as
Test stat = (Xbar - )/S/sqrt(n) = (18.04-20)/4.832/sqrt(8) = -1.96/1.7085 = -1.15


Related Solutions

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here is the data: 28.24, 28.39, 32.85, 19.96,   24.74,   13.88, 17.9,   24.41. He wishes to test the null hypothesis that the average amount of money people have...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data: 12, 31, 17, 18, 22, 36, 15, 13. Find the upper bound of a 95% confidence interval for the true mean amount of...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data: 27, 22, 11, 19, 20, 19, 25, 21. Find the upper bound of a 95% confidence interval for the true mean amount of...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data: 19, 21, 14, 19, 20, 17, 25, 15. Find the upper bound of a 95% confidence interval for the true mean amount of...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data: 13.66, 41.35, 21.43, 10.49, 25.57, 37.04, 17.5, 27.07. Find the lower bound of a 98% confidence interval for the true mean amount of...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...
Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here is the data: 29.34, 24.88, 28.5, 12.02,   13.45,   13.41, 10.03,   25.09. He wishes to test the null hypothesis that the average amount of money people have...
A retail chain (such as Macy’s) wants to determine the average amount of money which, in...
A retail chain (such as Macy’s) wants to determine the average amount of money which, in December, customers charge to their Macy’s credit card. A random sample of 100 cards is selected and sample mean = $730, with sample standard deviation = $200. a - Build a 95% confidence interval for the mean b - What should the sample size be if the 95% confidence interval were to have a margin error of $30? c - Assume that μ =...
The Australian Automobile Association wants to estimate the amount of money spent annually by all its...
The Australian Automobile Association wants to estimate the amount of money spent annually by all its members for transportation costs. A sample of 25 members reported the following dollar amounts for transportation costs last year: 734 769 687 689 759 752 739 694 736 700 768 693 713 732 712 700 707 730 711 700 703 710 682 753 706 (Round your answers to 2 decimal places.) Find a) the point estimate for the population mean, b) the point estimate...
Maria is a waitress at Dreck burgers. She wants to estimate the average amount each table...
Maria is a waitress at Dreck burgers. She wants to estimate the average amount each table leaves for a tip. A random sample of 5 groups was taken and the amount they left for a tip (in dollars) is listed below: $11.00 $7.00 $7.00 $5.00 $10.00 A) What is the mean of the data? B) What is the standard deviation of the data? (Use two decimal places) C) Find a 95% confidence interval for the average amount left by all...
true or false? 16) Reliance on expert opinion to predict consumer behavior has the advantage of...
true or false? 16) Reliance on expert opinion to predict consumer behavior has the advantage of being a relatively low cost approach to gathering information. In many situations, however, it is subject to several sources of bias that can undermine its reliability. Answer: 17) Cross-section data observed at several points in time are called inverted data. Answer: 18) The coefficient of determination is the proportion of the variation that is not explained by the regression model. Answer:
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT