Hypothesis and type error testing. Z score?

Question

1. Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not.

Answer 1

Step 1 :

The hourly wage of the babysitter is $ 12 per hour.

Mean wage in the area is $ 14 per hour.

Standard deviation is 1.9.

Calculate Z-score.

z - Score formula is .

where is hourly wage of the babysitter,

is the mean and

is the standard deviation.

The Z-score is -1.05.

Step 2 :

Find the probability that babysitter wage is greater than $ 12 per hour, .

From z - score table the probability is .

The probability that babysitter wage is greater than $ 12 per hour is 0.8531.

Solution :

The Z-score is -1.05.

The probability that babysitter wage is greater than $ 12 per hour is 0.8531.