Question

a parenting magazine reports that the average amount of wireless data used by teenagers each month is 10 gb. for her science fair project, ella sets out to prove the magazine wrong. she claims that the mean among teenagers in her area is less than reported. ella collects information from a simple random sample of 25 teenagers at her high school, and calculates a mean of 9.1 gb per month with a standard deviation of 2.3 gb per month. assume that the population distribution is approximately normal. test ellas claim at the 0.05 level of significance. 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 population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Substitute the values

We are given that $\bar{x} = 9.1$, $\mu=10$, $s = 2.3$, and $n = 25$.
First, calculate $\frac{s}{\sqrt{n}}=\frac{2.3}{\sqrt{25}}=\frac{2.3}{5}=0.46$.
Then, calculate $t=\frac{9.1 - 10}{0.46}=\frac{- 0.9}{0.46}\approx - 1.957$.

Answer:

$-1.957$