1.In conducting a two-tailed hypothesisz-test, the test statistic was determined to bez=2.66.For which of the following values ofis the result statistically significant (that is, for whichshouldH0be rejected)?

Select all that apply:

• =0.100
• =0.020
• =0.200
• =0.010
• =0.050
• None of the above

2.Consider a population with a mean=19and standard deviation=74. Suppose random samples of sizen=63are selected from this population.

a)greater than 191.5 and less than 203.9?

b) greater than 191.5 given less than 203.9?

c) greater than 191.5 or greater than 203.9?

3.On a peer-to-peer (P2P) lending website, borrowers complete a approval scoring form that lenders use to assess creditworthiness. Lenders generally believe that borrowers who score at least74do not default on loans. Consequently, borrowers are ratedAif their overall score is at least74, otherwise they are ratedB.

A reasonably large sample of real borrower data was collected:

1. among those thatdid not defaulton their loans, initial approval scores were normally distributed with a mean of 80.4 and a standard deviation of 5.9.

11.among those thatdefaultedon their loans, initial approval scores were normally distributed with a mean of 69.2 and a standard deviation of 8.9.

Report each answer as a decimal (not percent) accurate to at least 4 decimal places. Answers from software or from roundedz-scores (to 2 decimal places) are accepted.

a)What proportion of borrowers that:

defaultedwere initially ratedB?

b)Among those thatdid not default, what is the probability that a borrower:

scored below 79.2 or above 81.8?

4.In constructing a confidence interval for a population mean, which of the following are true?

Select four (4) true statements from the list below:

• If a confidence interval does not contain the population parameter, then an error has been made in the calculation.
• If a confidence interval for the population mean is constructed from a sample of sizen=30, that interval must contain the sample mean.
• Decreasing the confidence level will increase the width of the confidence interval.
• A 97% confidence interval must capture 97% of the population values.
• For the same sample data, a 95% confidence interval will be wider than a 99% confidence interval.
• If the point estimate and upper limit for a confidence interval are 170.1 and 182.1 respectively, then the lower limit must be 12.
• If a particular 85% confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the 87% confidence level.

.. For a confidence level of 97%, the right-tail area/2 = 0.06.