Question

the dodge reports are used by many companies in the construction field to estimate the time required to complete various jobs. the company managers want to know if the time required to install 130 square feet of bathroom tile is different from the eight hours reported in the current manual. a researcher for dodge randomly selects 56 construction workers and determines the time required to install 130 square feet of bath tile. the average time required to install the tile for the sample is 6.8 hours with a standard deviation of 4.5 hours. use a hypothesis test to determine whether the managers assumptions are substantiated by the data. use a significance level of $alpha = 0.01$. assume the population of tile installation times is approximately normally distributed. step 2 of 3: compute the value of the test statistic. round your answer to three decimal places.

Explanation:

Step1: Identify the formula

The formula for the one - sample t - test statistic is $t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Identify the values

We are given that $\bar{x} = 6.8$, $\mu=8$, $s = 4.5$, and $n = 56$.

Step3: Compute the test statistic

Substitute the values into the formula:
\[

$$\begin{align*} t&=\frac{6.8 - 8}{\frac{4.5}{\sqrt{56}}}\\ &=\frac{- 1.2}{\frac{4.5}{\sqrt{56}}}\\ &=\frac{-1.2}{\frac{4.5}{7.4833}}\\ &=\frac{-1.2}{0.6013}\\ &\approx - 1.996 \end{align*}$$

\]

Answer:

$-1.996$