A random sample of patients at a hospital became part of a...

A random sample of patients at a hospital became part of a nutrition study on dietary habits. Part of the study consisted of a survey asking about types of foods consumed. Each of the questions was scored on a scale from one (most unhealthy) to five (most healthy ). The answers were averaged. A prior study conducted at the hospital showed that such averages follow a Normal distribution. The population of interest is the patients at the hospital. If researchers sample n = 20 subjects and wish to calculate a 90% confidence interval, the critical value t* is: A. 2.845 B. 2.861 C. 2.093 D .2.086 E. 1.725 F. 1.729 . A sample of n = 20 patients produced the following statistics: x(bar) = 3.3 and s = 1.2. The 90% confidence interval for the mean survey score is: A. (2.738, 3.682) B. (2.378, 4.222) C. (2.836, 3.764) D. (2.532, 4.068) E. (2.738, 3.861) F. (2.635, 3.965) .

Transcript

00:01 A random sample of patients at a hospital became part of the nutrition study on dietary habit.

00:06 So part of the study consisted of a serving asking about types of food consume.

00:12 Each question was scored on a scale from 1 to 5, so where one represents most unhealthy and 5 represents the most healthy.

00:22 The answers were averaged.

00:24 A prior study conducted at the hospital show that such average follows in normal distribution distribution.

00:31 So the population of interest is the patients at the hospital.

00:34 If researchers sample 20 subjects and wishes to calculate a 90 % confidence interval, what is the critical value? so that is the first question.

00:46 So for our first question, which is question one, our n is equals to 20.

00:50 Confidence level is equal to 90%.

00:54 Are you supposed to get the critical value, which is also a c critical value? so since our confidence level is 90%, our alpha level is going to be 10 % and that is 0 .10 now from the central limit theorem we can see that our sample size is not up to 30 this is a 20 a sample size less than 30 so that simply implies that we are going to be using a t distribution to define this beta sets because according to the central limit theorem when the sample size of a sampling distribution is greater than or equals to 30 we can definitely say that the data set is defined by a normal distribution but our sample size here is 20 it is not up to 30 so definitely we are going to use something close to the normal distribution and that is a t distribution so to get at a critical value for a t distributed data will be needed one we call the level of significance that is 0 .10 and the girl freedom which is the sample size minus 1 which is our 20 minus 1 which gives us 19 so once we have these two details ready we are good to go we are supposed to construct a confidence interval so that makes our tests to be a two -tailed test so yes my calculator to get the critical value we have a two -student we have two -tailed we have years to be 19 and we have yet to be 0 .10 and our answer is 1 .7 to 91 so our critical value for question 1 is 1 .7 to 9 -1 and that is simply option f so that is this option over here so option f so our answer is actually option f so our question two question two says that a sample of n is a cost to 20 patients produces the following statistics we have the x but to be cost 3 .3 we have the sample standard divisions because to 1 .2 so we are supposed to get the confidence the 90 % sense confidence interval so xxbis 3 .3 sample standard division is actually equals to 1 .2 we have our sample size n to be equals to 20 we've been able to get the critical value cv to be cost 1 .7 291 so that means to construct our confidence in time we have the formula that says mule is equals to x bar plus or minus the critical value times s divided by the square root of n so um is equal to we have 3 .3 plus or minus 1 .7 2 .91 times we have 1 .2 divided by the square out of 20...

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