Answered: A manager at a local discount gym…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

A manager at a local discount gym believes that less than 20% of gym members use the gym, at least 5 days a week. She randomly selects 100 gym members and tracks (using the electronic login system at the door) how many days they used the gym over the 2-week period. The following are the results:

2	3	10	4	2	3	8	4	8	10
5	0	6	3	9	13	6	3	12	5
3	3	5	1	5	9	8	5	8	2
6	4	4	2	12	1	3	3	2	12
7	3	14	2	8	5	2	6	1	5
6	9	6	8	10	1	11	3	2	1
5	4	1	2	3	13	7	4	8	3
7	4	3	2	10	3	1	7	11	8
4	7	6	7	8	11	7	6	3	2
5	0	4	6	5	12	2	10	1	2

Test the manager's claim at the 2.5% level of significance.

Standard Normal Distribution Table

a. Calculate the test statistic.

z=�=

Round to two decimal places if necessary

Enter 0 if normal approximation to the binomial cannot be used

b. Determine the critical value(s) for the hypothesis test.

Round to two decimal places if necessary

Enter 0 if normal approximation to the binomial cannot be used

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

Cannot Use Normal Approximation to Binomial

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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