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 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".

[tex]\bar X=8[/tex] represent the sample mean for the sample

[tex]\mu[/tex] 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:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=150-1=149[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], 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 [tex]t_{\alpha/2}=1.976[/tex]

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

[tex]8-1.976\frac{1}{\sqrt{150}}=7.83[/tex]

[tex]8+1.976\frac{1}{\sqrt{150}}=8.16[/tex]

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:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n} =8[/tex]

So then the best interpretation for this case would be:

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