You research the salaries of senior-level civil engineers and ...

Question

You research the salaries of senior-level civil engineers and find that the population mean is $131,935. In Exercise 4, does the t-value fall between -t0.95 and t0.95?

Accepted Answer

Hello, everyone, let's take a look at this question together. A wellness researcher is studying the average daily screen time of adults. In a previous analysis, a random sample of 10 adults showed a mean daily screen time of 5.38 hours with a standard deviation of 0.43 hours. The researcher claims that the population mean daily screen time is 5.2 hours. Assuming the population of screen times are normally distributed, determine whether the calculated T value falls between negative T sub 0.05 and T sub 0.05 at the 90% confidence level. Is it answer choice A, yes, answer choice B, no, or answer choice C, it cannot be determined. So in order to solve this question, we have to determine the calculated T value at the 90% confidence level to determine whether it falls between negative T 0.05 and T 0.05, assuming the population of screen times are normally distributed. And the first step in solving this problem is selecting the appropriate formula. And because the population standard deviation is unknown and the sample size is small, meaning a sample size less than 30, we use the T score formula to standardize the difference between the sample mean and the claimed population mean, which the T score formula is equal to the sample mean subtracted by the population mean divided by the sample standard deviation, which is divided by the square root of the. sample size and using the data provided in the question, we substitute the values, so our T score formula is equal to 5.38, subtracted by 5.2, divided by 0.43, which is divided by the square root of 10. And simplifying the values, our T score formula yields a value of approximately 1.324. And then we need to determine the critical T value. Which we know our degrees of freedom is calculated as N minus 1, so 10 minus 1 is equal to 9, so our degrees of freedom is 9, and from the T distribution table for 90% confidence, our critical T value is equal to 1.833. And then we need to compare the T values since we are determined. Whether our calculated T value falls between negative T sub 0.05 and T.05, which we know that our T value of 1.324 does in fact fall between -1.833 and 1.833, so the calculated T value falls between negative. T0.05 and T 0.05. Therefore, the correct answer is yes, the calculated T value does fall between negative T sub 0.05, and T sub 0.05 at the 90% confidence level, which looking at our answer choices, makes answer choice A the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

You research the salaries of senior-level civil engineers and find that the population mean is $131,935. In Exercise 4, does the t-value fall between -t0.95 and t0.95?

Key Concepts

Population Mean

t-Distribution

Hypothesis Testing

Watch next