Questions: An employment information service claims the mean annual salary for senior level product engineers is 99,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At alpha=0.01, test the claim that the mean salary is 99,000. Complete parts (a) through (e) below. Assume the population is normally distributed. Annual Salaries 100,627 96,301 93,591 112,783 82,571 74,234 77,022 80,943 102,417 76,200 104,072 104,036 91,077 82,162 85,025 110,222 (c) Find the standardized test statistic, t. The standardized test statistic is t= (Round to two decimal places as needed.)

An employment information service claims the mean annual salary for senior level product engineers is 99,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At alpha=0.01, test the claim that the mean salary is 99,000. Complete parts (a) through (e) below. Assume the population is normally distributed.

Annual Salaries
100,627 96,301 93,591 112,783
82,571 74,234 77,022 80,943
102,417 76,200 104,072 104,036
91,077 82,162 85,025 110,222

(c) Find the standardized test statistic, t.

The standardized test statistic is t=
(Round to two decimal places as needed.)

Transcript text: An employment information service claims the mean annual salary for senior level product engineers is $\$ 99,000$. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At $\alpha=0.01$, test the claim that the mean salary is $\$ 99,000$. Complete parts (a) through (e) below. Assume the population is normally distributed. \begin{tabular}{|rrrr|} \hline \multicolumn{4}{|c|}{ Annual Salaries } \\ \hline 100,627 & 96,301 & 93,591 & 112,783 \\ 82,571 & 74,234 & 77,022 & 80,943 \\ 102,417 & 76,200 & 104,072 & 104,036 \\ 91,077 & 82,162 & 85,025 & 110,222 \\ \hline \end{tabular} (c) Find the standardized test statistic, t . The standardized test statistic is $\mathrm{t}=$ $\square$ (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Calculate the sample mean

The sample mean (x̄) is the sum of all the salaries divided by the number of salaries (n=16).

x̄ = (100627 + 82571 + 102417 + 91077 + 96301 + 74234 + 76200 + 82162 + 93591 + 77022 + 104072 + 85025 + 112783 + 80943 + 104036 + 110222) / 16

x̄ = 90,908.8125

Step 2: Calculate the sample standard deviation

First calculate the squared difference between each salary and the sample mean. Then sum all those values. Finally divide by (n-1) and find the square root of that number.

s = sqrt(((100627-90908.8125)^2 + (82571-90908.8125)^2 + ... + (110222-90908.8125)^2) / (16-1))

s ≈ 13636.56

Step 3: Calculate the t-statistic

The t-statistic is calculated using the formula:

t = (x̄ - μ) / (s / sqrt(n))

Where μ is the claimed mean salary ($99,000), x̄ is the sample mean, s is the sample standard deviation and n is the sample size.

t = (90908.8125 - 99000) / (13636.56 / sqrt(16))

t ≈ -2.37