According to an estimate, the average total parent and student debt for new coll

Question

According to an estimate, the average total parent and student debt for new college graduates was $34,400 in 2010-11 (Time, October 31, 2011). A random sample of 500 of this year's graduates showed that their average such debt is $38,000 with a standard deviation of $5490. Do the data provide significant evidence at a 10% significance level to conclude that the current average total parent and student debt for new graduates is higher than $34,400? Use both the p-value approach and the critical-value approach Use the p-value approach. Use the t distribution table to find a range for the p-value. Enter the exact values for the range p-value

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 34400
Alternative hypothesis: > 34400

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

S= 5490

DF = n - 1

D.F = 499
t = (x - ) / SE

t = 0.66

tcritical = 1.285

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 0.66

Interpret results. Since the t-value (0.66) is less than the critical value (1.285), we have to accept the null hypothesis.

The current page total perent and student debt for new graduates is not higher than 34400.

p-value = 0.253

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