Question

1. A company selling licenses of new e-commerce software advertised that firms using this software could obtain, on average during the first year, a minimum yield (in cost savings) of 20 percent on average on their software investment. To disprove the claim, we checked with 10 different firms which used the software. These firms reported the following cost-saving yields (in percent) during the first year of their operations:

   {17.0, 19.2, 21.5, 18.6, 22.1, 14.9, 18.4, 20.1, 19.4, 18.9}.

   A. Do we have significant evidence to show that the software company’s claim of a minimum of 20 percent in cost savings was not valid? Test using α = 0.05
2. B. Compute a 95% confidence interval for the average cost-saving yield estimate.

Answer 1

Solution:-

a)

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

Null hypothesis: u > 20
Alternative hypothesis: u < 20

Note that these hypotheses constitute a one-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), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.65497
DF = n - 1

D.F = 9
t = (x - u) / SE

t = - 1.512

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.

The observed sample mean produced a t statistic test statistic of -1.512.

Thus the P-value in this analysis is 0.082.

Interpret results. Since the P-value (0.082) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that that the software company’s claim of a minimum of 20 percent in cost savings.

b) 95% confidence interval for the average cost-saving yield estimate is C.I = ( 17.528, 20.492).

C.I = 19.01 + 2.263*0.65497

C.I = 19.01 + 1.4822

C.I = ( 17.528, 20.492)