Question

You may need to use the appropriate appendix table or technology to answer this question.

The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute reported that entry level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011.† Assume the standard deviation for male graduates is $2.30, and for female graduates it is $2.05. (Round your answers to four decimal places.)

(a)

What is the probability that a sample of 60 male graduates will provide a sample mean within $0.50 of the population mean, $21.68?

(b)

What is the probability that a sample of 60 female graduates will provide a sample mean within $0.50 of the population mean, $18.80?

(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 $0.50 of the population mean? Why?

part (a), because the standard error is lowerpart (b), because the standard error is lower part (a), because the standard error is higherpart (b), because the standard error is higher

(d)

What is the probability that a sample of 130 female graduates will provide a sample mean less than the population mean by more than $0.30?

Answer #1

a)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 21.68 |

std deviation =σ= | 2.3000 |

sample size =n= | 60 |

std error=σ_{x̅}=σ/√n= |
0.2969 |

probability that a sample of 60 male graduates will provide a sample mean within $0.50 of the population mean, $21.68:

probability = | P(21.18<X<22.18) | = | P(-1.68<Z<1.68)= | 0.9535-0.0465= | 0.9070 |

b)

probability = | P(18.3<X<19.3) | = | P(-1.89<Z<1.89)= | 0.9706-0.0294= | 0.9412 |

c)

part (b), because the standard error is lower

d)

probability = | P(X<18.5) | = | P(Z<-1.67)= | 0.0475 |

The Economic Policy Institute periodically issues reports on
wages of entry-level workers. The institute reported that
entry-level wages for male college graduates were $21.68 per hour
and for female college graduates were $18.80 per hour in 2011.
Assume the standard deviation for male graduates is $2.30, and for
female graduates it is $2.05.
a) What is the probability that a sample of 50 male graduates
will provide a sample mean within $0.50 of the population mean,
$21.68?
b)What is the...

The Economic Policy Institute issues reports on wages of entry
level workers. The Institute reported that entry level wages for
male collge graduates were $21.68 per hour and for femail graduates
$18.80 per hour. Assume the SD for male grads is $2.30 and for
female grads $2.05.
a) What is the probability that a simple random sample of 50
male grads will provide a sample mean within fifty cents of the
population mean $21.68?
b) What is the probability that...

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