Question

the economic policy institute periodically issues reports on workers' wages. suppose the institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. assume the standard deviation for male graduates is $4.60 and for female graduates it is $4.10. (round your answers to four decimal places.) (a) what is the probability that a sample of 40 male graduates will provide a sample mean within $1.00 of the population mean, $37.39? 0.1703 (b) what is the probability that a sample of 40 female graduates will provide a sample mean within $1.00 of the population mean, $27.83? (c) in which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? why? part (a), because the standard error is higher part (b), because the standard error is lower part (b), because the standard error is higher part (a), because the standard error is lower (d) calculate the amount that is $0.60 less than the population mean of $27.83. what is the probability that a sample of 130 female graduates will provide a sample mean less than this amount?\

Answer 1

The probability that a sample of 40 female graduates will provide a sample mean within $1.00 of the population mean is approximately 0.3174.

Step-by-step explanation:

(b) To find the probability that a sample of 40 female graduates will provide a sample mean within $1.00 of the population mean, $27.83, we can use the standard normal distribution. First, we calculate the standard error using the formula:

Standard Error = Standard Deviation / sqrt(Sample Size) = 4.10 / sqrt(40) = 0.6482

Next, we need to find the z-score corresponding to a sample mean within $1.00 of the population mean. We can use the formula:

z-score = (Sample Mean - Population Mean) / Standard Error = (27.83 - 27.83) / 0.6482 = 0

Finally, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 0, which is 0.5000. However, since we are interested in the probability of obtaining a sample mean within $1.00 of the population mean, we need to find the area between -1.00 and 1.00, which is the same as finding the area to the right of -1.00 and subtracting it from the area to the right of 1.00. This gives us a probability of approximately 0.3174.