An employer claims that full time employees have a mean income of $35,000. A sample of 200 employees were considered. Their mean salaray was
$34,000. POP sd of $4,000. Does her claim seem reasonable at at 0.05 significance level?
To determine whether the employer's claim seems reasonable, we can conduct a hypothesis test. Here's how to do it:
Step 1: State the hypotheses.
- Null hypothesis (H₀): The mean income of full-time employees is $35,000.
- Alternative hypothesis (H₁): The mean income of full-time employees is not $35,000.
Step 2: Set the significance level (α).
In this case, the significance level is given as 0.05, which means we're willing to accept a 5% chance of rejecting the null hypothesis incorrectly.
Step 3: Calculate the test statistic.
To calculate the test statistic, we'll use the formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Given:
Sample mean (x̄) = $34,000
Population mean (μ) = $35,000
Population standard deviation (σ) = $4,000
Sample size (n) = 200
Plugging in the values, we get:
t = (34,000 - 35,000) / (4,000 / sqrt(200))
Step 4: Find the critical value.
Since our alternative hypothesis is two-tailed (not equal to $35,000), we'll need to find the critical values from the t-distribution table based on our significance level (α) and degree of freedom (n - 1 = 199).
Step 5: Compare the test statistic with the critical value.
If the test statistic falls within the critical value range, we fail to reject the null hypothesis. Otherwise, if the test statistic falls outside the critical value range, we reject the null hypothesis.
If the test statistic is less extreme (i.e., closer to zero) than the critical value(s) in either tail, we fail to reject the null hypothesis.
So, perform the calculations to find the test statistic and critical value(s). Then you can compare them to make a conclusion about whether the employer's claim seems reasonable or not.