Television A researcher wanted to determine the mean number of...

Question

Television A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey I indicate that s = 7.5 hours.

c. What effect does doubling the required accuracy have on the sample size?

a. How many people are needed to estimate the number of hours people watch television per week within 2 hours with 95% confidence?

Accepted Answer

Welcome back, everyone. In this problem, a nutritionist wants to estimate the average number of servings of vegetables consumed per week by adults. Previous studies suggest the standard deviation is S equals 5.2 servings. How large a sample is needed to estimate the mean number of servings within 1.5 servings with 95% confidence. AS 45, B 47, C 54, and D 58. No, to determine the sample size needed to estimate the mean average number of servings, recall that our sample size n in a confidence interval for the population mean is equal to the critical Z value. OK, in this case, our critical Z value for a 95% confidence level multiplied by the estimated standard deviation of the populations divided by E the desired margin of error. In our problem Oh, all squared, my apologies. We're in our problem. As, as we said, is 5.2 servings. And the desired margin of error, is 1.5 servings. Now, so far, since we know S and E, all we need to do is to figure out our critical Z value and then we'll be able to solve. How can we do that? Well, for a 95% confidence level. OK. Then our significance level would be equal to 1 minus 95% or 0.95, which equals 0.05. Thus, that means that half of our half of alpha or half of our significance level will be 0.025. So what this means then is that from the standard normal distribution table. Then, so let's write that thought from a standard. Normal distribution table, or you could use your calculator to get this value as well if it has that capability. Then our critical Z value here, the alpha of 0.025 is going to be equal to approximately 1.96. So now that we have this value, we can solve for our sample size. Because no, that means our sample size N will be equal to 1.96 multiplied by 5.2, divided by 1.5, or squared. And when we solve here, we should get that to be approximately 46.2. However, we need to, the sample size must be a whole number, right? So we can round up to the next integer. Thus, the required sample size is 47 N equals 47. If we look back at our answer choices, that means B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Watch next