The standard IQ test has a mean of 96 and a standard...

The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 99% certain that we are within 4 IQ points of the true mean. Determine the required sample size. 82 1 178 10 Construct a 99% confidence interval for the population mean, ?. Assume the population has a normal distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years. 19.9 to 24.9 17.2 to 23.6 16.3 to 26.9 18.7 to 24.1

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:07 In this question we're going to discuss about the confident interval for the mean.

00:12 Here let me remind you that the confident interval for the mean, it will be the two cases where we have the sigma is known.

00:26 And the second case when the sigma is unknown.

00:30 When the sigma is known, we will have the formula will be the xb plus or minus z n4 over 2, times with the sigma over square of n.

00:42 When the sigma is unknown, it will be the x bar plus or minus t degree of freedom equal to n minus 1, and 4 over 2, and then times s over square of n.

00:56 Now in this question 16, we are given the meaning standard deviant, mew and the standard division sigma.

01:06 One to be 99 % certain that we are within the 4 iq point.

01:12 So in this formula, this quantity is called the matching error.

01:18 Also this one will be called the matching error as well.

01:22 So therefore the question asked nature of the matching error equal to the 4.

01:27 And once you be 99 % it means that the alpha equal to 1%.

01:32 Therefore and far over 2 equal to the 0 .5 % equal to the 0 .005.

01:41 If we look up the table, the z of the 0 .005, it will equal to the 2 .575.

01:52 Now because here we know the two population standard deviation, therefore in the question 16 we use the first formula here.

02:00 And the margin error in the first formula we have it will equal to the zan4 over 2 will be 2 .575 times sigma will be the 14 over the square of n we don't know that's what we want to find equal to 4 so from here want you find the square of n equal to the 2 .575 times with the 14 divided by 4 and then we get equal to it will remove the square root on the end we have to square this one up so we get equal to the times 14 divided by 4 square the answer up equal to the 81 .2 3 normally for this sample size we will route it up to the 82 therefore the answer will be the first option here now for the question 17, we want to gain 99 % complete for the population mean, assume the population has a normal distribution.

03:07 And we will have the n equal to the 19 now, the x -par equal to the 22 .4...

Question

Please give Ace some feedback