According to a 2021 survey of student loan debt incurred to finance undergraduate education, the average amount of debt for a 4-year college degree with $37,172 with a standard deviation of $9,250. The sample size is 1,000. Inputs $ Sample Mean (X̅) $37,172 Presumed Population Standard Deviation, σ $9,250 Please Note: The t-value with 999 degrees of freedom is 1.962. The formula in Excel is =TINV(0.05,999). You cannot find this value on the Student-t table. What is the point estimate for the population mean, μ? Point Estimate for the population mean, μ = What is the appropriate z-value to use when constructing a confidence interval at a 95% and 99% confidence levels? Use the z-value table and Microsoft Excel. Confidence Level z-Value (Table) z-Value (Excel) Excel Formula 95% (0.90) =ABS(NORM.S.INV(0.025)) 99% (0.99) =ABS(NORM.S.INV(0.005)) What is the appropriate t-value to use when constructing a confidence interval at a 95% and 99% confidence levels using Excel TINV function. Use Microsoft Excel to find the t-values as they will not be on the Student-t table. Confidence Level t-Value (Excel) Excel Formula 95% (0.95) =TINV(1-.95,df) 99% (0.99) =TINV(1-.99,df)

Question

According to a 2021 survey of student loan debt incurred to finance undergraduate education, the average amount of debt for a 4-year college degree with $37,172 with a standard deviation of $9,250. The sample size is 1,000.

Inputs	$
Sample Mean (X̅)	$37,172
Presumed Population Standard Deviation, σ	$9,250

Please Note: The t-value with 999 degrees of freedom is 1.962. The formula in Excel is =TINV(0.05,999). You cannot find this value on the Student-t table.

What is the point estimate for the population mean, μ?

Point Estimate for the population mean, μ =

What is the appropriate z-value to use when constructing a confidence interval at a 95% and 99% confidence levels? Use the z-value table and Microsoft Excel.

Confidence Level	z-Value (Table)	z-Value (Excel)	Excel Formula
95% (0.90)			=ABS(NORM.S.INV(0.025))
99% (0.99)			=ABS(NORM.S.INV(0.005))

What is the appropriate t-value to use when constructing a confidence interval at a 95% and 99% confidence levels using Excel TINV function. Use Microsoft Excel to find the t-values as they will not be on the Student-t table.

Confidence Level

t-Value (Excel)

Excel Formula

95% (0.95)

=TINV(1-.95,df)

99% (0.99)

=TINV(1-.99,df)

Using a z-values calculate the confidence interval using at a 95% and 99% confidence levels. Do this by hand and use Excel’s CONFIDENCE.NORM function.

Using a t-values calculate the confidence interval using at a 95% and 99% confidence levels. Do this by hand and use Excel’s CONFIDENCE.T function. Assume the sample standard deviation is $9,250.

What does these confidence intervals you constructed tell you?

Compare the confidence intervals created using z-values and student-t. What are the big differences?

Confidence Intervals are used to estimate unknown population parameters. Which standardized score is more appropriate: z-values or student-t? Explain your answer.