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According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduates from public universities had student loans. We randomly select 50 students at a time. Flag this Question Question 15 pts What is the mean of the distribution of sampling proportions? Do not round, and enter your answer as a proportion (decimal number) not a percentage. Flag this Question Question 25 pts What is the standard error for the distribution of sampling proportions? If necessary, round to three decimal places.

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Answer:

The mean of the sampling proportions is 0.62.

The standard error for the distribution of sampling proportions is 0.069.

Step-by-step explanation:

The proportion of graduates from public universities that had student loans is p=0.62.

The sampling distribution of the proportions, if the sample are of size n=50, has the following parameters:

[tex]\mu=p=0.62\\\\\sigma=\sqrt{\frac{p(1-p)}{n} } =\sqrt{\frac{0.62*0.38}{50} } =\sqrt{0.004712}=0.069[/tex]

The mean of the sampling proportions is 0.62.

The standard error for the distribution of sampling proportions is 0.069.