Question

Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution and interpret. A sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of 0.78.

• You must show the shaded region.
• Give the calculator keystrokes for how you got the critical value for the regions.
• You must show the formula for the appropriate confidence interval, show the plugging in
of values, then use the calculator to find the interval.
• Give the calculator keystrokes for the interval.

Answer 1

The t-critical values for a two-tailed test, for a significance level ofα=0.1 are

tc​=−1.761 and tc​=1.761

Graphically

So t value for 90% CI is 1.761

So MArgin of Error is

Hence CI is