1. A sample of 150 Publix cashiers showed a mean hourly wage of $ 8.00, with a standard deviation of $ 1. Give an interval that is likely to contain about 95% of the sampled cashiers’ hourly wages.

A. (5, 10)
B. (6, 10)
C. (7, 9)
D. (6, 9)

2. Practically interpret the sample mean (x-bar) from the question above.

A. 95% of the sampled cashiers will have an hourly wage that falls at $ 8.00 per hour.
B. Each cashier can earn $ 8.00 per hour.
C. The mean hourly wage of the sampled cashiers is $ 8.00 per hour.
D. The true hourly wage for the Publix cashiers is $ 8.00 per hour.

a)    

So on this case the 95% confidence interval would be given by (7.83;8.16)

So then the best option seems to be:

C. (7, 9)

b) The mean calculated comes from the following formula:

So then the best interpretation for this case would be:

C. The mean hourly wage of the sampled cashiers is $ 8.00 per hour.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,149)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (7.83;8.16)

So then the best option seems to be:

C. (7, 9)

Part b

The mean calculated comes from the following formula:

So then the best interpretation for this case would be:

C. The mean hourly wage of the sampled cashiers is $ 8.00 per hour.

tangent

step-by-step explanation: