Question

it currently takes users a mean of 44 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 44 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 47.8 minutes with a standard deviation of 10.2 minutes. perform a hypothesis test at the 0.10 level of significance to see if the mean installation time has changed. step 2 of 3: compute the value of the test statistic. round your answer to three decimal places.

Explanation:

Step1: Identify the formula for the test - statistic

For a one - sample z - test (since $n = 51\geq30$), the formula is $z=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Substitute the given values

We are given that $\bar{x}=47.8$, $\mu = 44$, $s = 10.2$, and $n = 51$.
First, calculate $\frac{s}{\sqrt{n}}=\frac{10.2}{\sqrt{51}}\approx\frac{10.2}{7.1414}\approx1.4283$.
Then, $z=\frac{47.8 - 44}{1.4283}=\frac{3.8}{1.4283}\approx2.660$.

Answer:

$2.660$