Question

It currently takes users a mean of 25 minutes to install the most popular computer program made by RodeTech, a software design company. After changes have been made to the program, the company executives want to know if the new mean is now different from 25 minutes so that they can change their advertising accordingly. A simple random sample of 51 new customers are asked to time how long it takes for them to install the software. The sample mean is 26.2 minutes with a variance of 16 minutes. Perform a hypothesis test at the 0.01 level of significance to see if the mean installation time has changed. What kind of problem is this

Answer 1

Testing the hypothesis in this problem which is a two-tailed test, we can conclude that there is not sufficient evidence to conclude that the mean time of installation has changed, since the p-value of the test is 0.0364 > 0.01,

At the null hypothesis, we test if the mean is of 25 minutes, that is:

$H_0: \mu = 25$

At the alternative hypothesis, we test if the mean has changed, that is, if it is different than 25 minutes.

$H_1: \mu \neq 25$

We have the standard deviation for the sample, thus, the t-distribution is used. The value of the test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which:

• X is the sample mean.
• $\mu$ is the value tested at the null hypothesis.
• s is the standard deviation of the sample.
• n is the sample size.

In this problem:

• 25 is tested at the null hypothesis, thus $\mu = 25$.
• Sample mean of 26.2 minutes, thus $X = 26.2$.
• Sample of 51, thus $n = 51$.
• Variance of 16, thus $s = \sqrt{16} = 4$.

The value of the test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{26.2 - 25}{\frac{4}{\sqrt{51}}}$

$t = 2.14$

• The p-value of the test is found using a two-tailed test(test if the mean is different of a value), with t = 2.14 and 50 degrees of freedom.

• Using a t-distribution calculator, this p-value is of 0.0364.

Since the p-value of the test is 0.0364 > 0.01, there is not sufficient evidence to conclude that the mean time of installation has changed.

A similar problem is given at brainly.com/question/23777908