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Brittney N.

Elementary Statistics a Step by Step Approach

7 months, 2 weeks ago

So our question says a random sample of 16 subject was asked to perform a given tax at the time in seconds it took for each of them to complete the taxes recorded. So if we assume that it comes at the completion times are normally distributed. Find a 95% interval for the true mean completion time for the tax Then find the lower and upper limits of the 95% confidence interval. So to construct a 95% confidence interval for a single value of population means we have the formula that says meal is equals to x box plus or minus the critical value times the value by this crowd of Now we don't have the values. We only know that the sample size N is across to 16. We don't have the value of the sample mean we don't have developed a sample star division. We don't have the value of the critical value. So let's start by getting the value of the sample in a sample standard division. I was able to extract out each of these 16 data points and slot it into a calculator. We have a sample size to be 16. We have the sample mints with 30 points 39.063. We have the supplements with 39.63. And we have the sample standard division is to be closed to uh eight points four three. So this is a 8.43. So the next step is for us to get the critical value. The critical value is dependent on the type of distributional defense. Our dataset according to the central limit sir. When the sample size of the sampling distribution is greater than or equal to 30, we have ah The data set to be normally distributed but going to our sample size we have a sample size of 16, 16 is lesser than 30. So hence we are concluding that our data set is normally is not normally distributed. Hence they are going to be using a distribution. That simply implies that the critical value CV is going to be AT score. Now to get this caveat the critical value, we need our level of significance and that is going to be 5%. We need a degree of freedom. That is the sample size -1 which is 16 -1, which gives us 15. So from this we will be able to get the critical value. So we change this to teach students, this is a two tailed degree of freedom is 15 and a level of significance is 0.05 And that was 2.1314. Critical value is 2.13 14. So let's substitute the parameters. So we have the musicals to 39.063 Plus or -2.1314 Times 8.43 divided by the square root of 16. So we have musicals to 39.063 Plus or -2.1314 Times It's .43. It's once for three Divided by scrolls of 16, 2.1075. So mu is equal to 39.063 Plus or -2.1075 times 2.13 14. And there's a 4.41919. So we have our meal to be close to 39.063 Plus 4.4919. Or meal is a cost of 39.06, 3 -4 points 4919. So I will do the match four points 4919 Plus 39.063. And there was a 43.56 and started to decimal place or meals because when we subtract that We have 34 .57, so 95% confidence interval, it's actually across to 34.57 And 43.56. So this is the lower limit and this is the upper limit

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