Question

1) An advertisement for a headache remedy claims that on average headache sufferers find relief with this product in 15 minutes with a standard deviation of 2.3 minutes. A truth-in-advertising agency is considering a suit for false advertising and obtains a sample of 47 individuals, which shows that relief comes in average in 30 minutes and even longer. Can this suit be justified?

2) A particular corporation claims that over the past few years it has implemented a number of programs to boost the average salary of its Hispanic males, and that the positive results of these programs are evidenced by their Hispanic males’ average weekly earnings which surpassed the national average for Hispanic males. Its corporate figures come from a 2017 sample of 28 Hispanic male employees where the average weekly salary was $725 with s = $68. At a significance level of .01, do the data present sufficient evidence of the corporation’s claim? Average National Mean is 690

Answer 1

Solution:-

2)

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

Null hypothesis: u < 690
Alternative hypothesis: u > 690

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. 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).

SE = s / sqrt(n)

S.E = 12.851

DF = n - 1

D.F = 27
t = (x - u) / SE

t = 2.72

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 one-tailed test, the P-value is the probability that the t statistic having 27 degrees of freedom greater than 2.72.

Thus, the P-value = 0.006

Interpret results. Since the P-value (0.006) is less than the significance level (0.01), we have to reject the null hypothesis.