According to a study several years ago by the Personal Communications Industry Association, the average wireless phone user earns $62,600 per year. Suppose a researcher believes that the average annual earnings of a wireless phone user are now higher and he sets up a study to prove his theory. He randomly samples 48 wireless phone users and finds the average annual salary for this sample is $64,820 with a standard deviation of $7,810. Use to test the researcher’s theory.

Z = (mean1-mean2)/sqrt(SEm1^2 + SEm2^2)

SEm = SD/sqrt(n-1)

If only one SD is known, it can be used alone.

Look up Z in table in the back of your stats text labeled something like "areas under normal distribution to find proportion.

HA idk

-1.97

this question is correct or wrong?

To test the researcher's theory, we can use a hypothesis test. Specifically, we can use a one-sample t-test because we are comparing the sample mean to a known population mean.

Let's define our hypotheses:

Null hypothesis (H0): The average annual earnings of wireless phone users are still $62,600.
Alternative hypothesis (Ha): The average annual earnings of wireless phone users are higher than $62,600.

Next, we need to calculate the test statistic. The formula for the t-test statistic for a one-sample t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

In this case, the sample mean is $64,820, the population mean is $62,600, the sample standard deviation is $7,810, and the sample size is 48.

t = (64820 - 62600) / (7810 / sqrt(48))

Now we can calculate the t-value using a calculator or software. Assuming a significance level (alpha) of 0.05, we can compare this t-value to the critical value to determine if we reject or fail to reject the null hypothesis.

The critical value can be found using a t-distribution table or a calculator. For a one-tailed test (since we are testing for the average to be higher), with 48 degrees of freedom and a significance level of 0.05, the critical value is approximately 1.677.

If the calculated t-value is larger than the critical value, we reject the null hypothesis. If it is smaller, we fail to reject the null hypothesis.

Finally, comparing the calculated t-value to the critical value and interpreting the result would determine if the researcher's theory holds or if there is evidence to suggest that the average annual earnings of wireless phone users have increased.