Question

1. A random sample of 2,500 students is taken from the population of all part-time students in the United States, for which the overall proportion of females is 0.6.

There is a 95% chance that the sample proportion (p̂) falls between ______ and _______.

2. The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2009-2010 was $2,450. Assume that the standard deviation in Pell grant awards was $520.

If we randomly sample 40 Pell grant recipients and record the mean Pell grant award for the sample, then repeat the sampling process many, many times, what is the mean and standard deviation of the sample means?

Round your answers to the nearest dollar. Do not include commas in your answer.

Mean:

Standard Deviation:

3. The annual salary of teachers in a certain state X has a mean of $54,000 and standard deviation of σ = $6000.

What is the probability that the mean annual salary of a random sample of 32 teachers from this state is less than $53,000?

Round your answer to four decimal places.

Answer 1

Refer Z-table or use excel function "=NORM.S.INV((1-0.05))" to find the Z-value.

There is a 95% chance that the sample proportion (p̂) falls between and .

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Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-0.94, TRUE)" to find the probability.

The probability that the mean annual salary of a random sample of 32 teachers from this state is less than $53,000 is