Question

A study reports that recent college graduates from New Hampshire face the highest average debt of $31,630 (The Boston Globe, May 27, 2012). A researcher from Connecticut wants to determine how recent undergraduates from that state fare. He collects data on debt from 40 recent undergraduates. A portion of the data is shown in the accompanying table. Assume that the population standard deviation is $5,000.

Debt	Debt
24,045	23,911
19,150	24,036
26,756	19,159
31,924	26,764
31,529	31,921
34,211	31,531
14,622	34,212
24,371	14,629
31,011	37,425
20,112	22,267
22,092	33,843
17,095	17,482
16,311	28,239
20,658	30,047
21,668	35,133
14,951	25,113
22,700	22,917
23,526	28,922
26,221	23,640
23,713	29,335

Construct the 90% confidence interval for the mean debt of all undergraduates from Connecticut. (Do not round intermediate calculations. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

b. Use the 90% confidence interval to determine if the debt of Connecticut undergraduates differs from that of New Hampshire undergraduates.

• The debt of Connecticut undergraduates differs from that of New Hampshire undergraduates.

• The debt of Connecticut undergraduates does not differ from that of New Hampshire undergraduates.

Answer 1

a)

Sample mean using excel function AVERAGE(), x̅ = 25179.8

σ = 5000

n = 40

90% Confidence interval :

At α = 0.1 two tailed critical value, z_c = ABS(NORM.S.INV(0.1/2)) = 1.645

Lower Bound = x̅ - z_c*σ/√n = 25179.8 - 1.645 * 5000/√40 = 23879.4290

Upper Bound = x̅ + z_c*σ/√n = 25179.8 + 1.645 * 5000/√40 = 26480.1710

23879.429 < µ < 26480.171

b)

As the confidence interval do not contain 31630, we reject the null hypothesis.

The debt of Connecticut undergraduates differs from that of New Hampshire undergraduates.