Question

Dell claims that their new computer can successfully run 12 Microsoft programs at one time give or take 2 programs. A group of students wanting to test this claim decide to conduct an experiment. Students took 30 laptops and found that the units can run on average 8 programs at one time.

Answer 1

Solution:-

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

Null hypothesis: u = 12
Alternative hypothesis: u $\neq$ 12

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 z-test.

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

SE = s / sqrt(n)

S.E = 0.36515
z = (x - u) / SE

z = - 10.95

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 -10.95 or greater than 10.95.

Thus, the P-value = less than 0.001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that new computer can successfully run 12 Microsoft programs at one time.