Question

It is stated that the average costof books and supplies for a college student is $402 with a population standard deviation of $138.  You would like to test this claim at the level of significance of .05.  Using a simple random sample of 50 college students an average of $451 was computed.  

State the null hypothesis

State the alternative hypothesis

Calculate the test statistic

Calculate the p-value

What conclusion will you draw?

Repeat the hypothesis test using the critical value approach?

What sample mean would we need to get to start to reject the null hypothesis?

Answer 1

Solution:-

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

Null hypothesis: u = 402
Alternative hypothesis: u $\neq$ 402

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 19.5162

z = (x - u) / SE

z = 2.51

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

Since we have a two-tailed test, the P-value is the probability that the z statistic less than -2.51 or greater than 2.51.

Thus, the P-value = 0.012.

Interpret results. Since the P-value (0.012) is less than the significance level (0.05), we have to reject the null hypothesis.

Critical value approach

z = 2.51

zcritical = + 1.96

Rejection region is - 1.96 < z < 1.96

Interpret results. Since the z-value (2.51) lies in the critical region, hence we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the average costof books and supplies for a college student is $402.