Week 6 Exploratory Data Analysis Part B
MATH533
Applied Managerial Statistics
Table of Contents
1 . Hypothesis Testing and Confidence Interval ……………………………………………………………. 3
a. Mean sales per week exceeds 41.5 per salesperson.…………………………………………….…....3
b. Proportion receiving online training is less than 55% ….……………………………………………4
c. Mean calls made among those with no training is less than 145 .……………………………….4
d. Mean time per call is greater than 15 minutes ………………………………………….…..……...…..5
2. 99% confidence intervals …………………………………………………….………………………….………..6
, Hypothesis Testing and Confidence Intervals
1. Complete the hypothesis using α = 0.05 each
a. Mean sales per week exceeds 41.5 per salesperson
The Null Hypothesis: The mean sales per week are less than or equal to 41.5 per salesperson.
The Alternative Hypothesis: The mean sales per week are greater than 41.5 per salesperson.
Test Static: We will use z test and at a=0.05, the value of z statistic is 1.645.
Rejection region: If the calculated value of z is greater than 1.645, then we reject the null
hypothesis.
Assumptions: The scale of measurement is either interval or ratio (approximately interval) and
the characteristic is normally distributed in the population. Moreover, the random sampling is
performed from a defined population.
Characteristic
Calculation of test static:
z
Conclusion:
The p value is 0.240. Since, 0.704 < 1.645, we do not reject the null hypothesis. This means the
results are statistically insignificant. It means that the mean sales per week is less than or equal
to 41.5 per salespersons.
b. Proportion receiving online training is less than 55%
The Null Hypothesis: The proportion receiving online training is greater than or equal to 55%.
The Alternative Hypothesis: The proportion receiving online training is less than 55%.
Test Static: We will use z test and at a=0.05, the value of z statistic is -1.645.
Rejection region: If the calculated value of z is less than -1.645, then we reject the null
hypothesis.
Assumptions: The scale of measurement is either interval or ratio (approximately interval) and
the characteristic is normally distributed in the population. Moreover, the random sampling is
performed from a defined population.
MATH533
Applied Managerial Statistics
Table of Contents
1 . Hypothesis Testing and Confidence Interval ……………………………………………………………. 3
a. Mean sales per week exceeds 41.5 per salesperson.…………………………………………….…....3
b. Proportion receiving online training is less than 55% ….……………………………………………4
c. Mean calls made among those with no training is less than 145 .……………………………….4
d. Mean time per call is greater than 15 minutes ………………………………………….…..……...…..5
2. 99% confidence intervals …………………………………………………….………………………….………..6
, Hypothesis Testing and Confidence Intervals
1. Complete the hypothesis using α = 0.05 each
a. Mean sales per week exceeds 41.5 per salesperson
The Null Hypothesis: The mean sales per week are less than or equal to 41.5 per salesperson.
The Alternative Hypothesis: The mean sales per week are greater than 41.5 per salesperson.
Test Static: We will use z test and at a=0.05, the value of z statistic is 1.645.
Rejection region: If the calculated value of z is greater than 1.645, then we reject the null
hypothesis.
Assumptions: The scale of measurement is either interval or ratio (approximately interval) and
the characteristic is normally distributed in the population. Moreover, the random sampling is
performed from a defined population.
Characteristic
Calculation of test static:
z
Conclusion:
The p value is 0.240. Since, 0.704 < 1.645, we do not reject the null hypothesis. This means the
results are statistically insignificant. It means that the mean sales per week is less than or equal
to 41.5 per salespersons.
b. Proportion receiving online training is less than 55%
The Null Hypothesis: The proportion receiving online training is greater than or equal to 55%.
The Alternative Hypothesis: The proportion receiving online training is less than 55%.
Test Static: We will use z test and at a=0.05, the value of z statistic is -1.645.
Rejection region: If the calculated value of z is less than -1.645, then we reject the null
hypothesis.
Assumptions: The scale of measurement is either interval or ratio (approximately interval) and
the characteristic is normally distributed in the population. Moreover, the random sampling is
performed from a defined population.
