Pedro is a salesman for a department store. He earns a commission of 8.5% on his sales. If he sold $1,200 in merchandise, what w
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Answer:
Assuming a significance level of we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane
Step-by-step explanation:
Data given
Our notation on this case :
represent the sample size for people who used a self service
represent the sample size for people who used a cashier
represent the sample mean for people who used a self service
represent the sample mean people who used a cashier
represent the sample standard deviation for people who used a self service
represent the sample standard deviation for people who used a cashier
Assumptions
When we have two independent samples from two normal distributions with equal variances we are assuming that
The statistic is given by:
And t follows a t distribution with degrees of freedom and the pooled variance
is given by this formula:
System of hypothesis
Null hypothesis:
Alternative hypothesis:
This system is equivalent to:
Null hypothesis:
Alternative hypothesis:
We can find the pooled variance:
And the deviation would be just the square root of the variance:
The statistic is given by:
The degrees of freedom are given by:
And now we can calculate the p value with:
Assuming a significance level of we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane