Q2 given the following gpa for 6 students 280 320 375 310...

Q2. Given the following GPA for 6 students: 2.80, 3.20, 3.75, 3.10, 2.95, 3.40 a) Calculate a 95% confidence interval for the population mean GPA. b) If the confidence level is increased from 95% to 99%, will the length of the confidence interval increase, decrease, or remain the same?

Transcript

00:01 In the a part, we have to obtain 95 % confidence interval for the population mean gpa.

00:08 We know that confidence interval is the range of value that consists of population parameter.

00:13 Confidence interval can be obtained by the formula x -bar plus or minus t alpha -by -2 into s upon square root of l.

00:22 Here, our first task is to obtain the value of sample mean and sample standard deviation.

00:28 Sample mare can be obtained by the formula summation xi divided by n which is equals to 2 .80 plus 3 .20 plus 3 .75 plus 3 .10 plus 2 .95 plus 3 .40 divided by 6 which is equals to 19 .2 divided by 6 which is equal to 19 .2 divided by 6 which is equal to x bar is equal to 3 .2.

01:03 The sample standard deviation s can be obtained by the formula.

01:07 Summation xi minus x bar whole bracket square divided by n minus 1, where xi minus x bar whole backet square is known as square deviation.

01:18 In order to obtain this square deviation, subtract value of mean that is 3 .2 from each observations and then take a square of it.

01:31 Here it is the table which represent operation.

01:35 Therefore s is equal to 0 .575 divided by n minus 1 is 6 minus 1, which is equals to square root of 0 .575 divided by 5, which is equals to s is equal to 0 .3391.

01:59 Next task is to obtain the value of t alpha by 2.

02:03 We know that t distribution has n minus 1 degrees of freedom...

Question

Q2. Given the following GPA for 6 students: 2.80, 3.20, 3.75, 3.10, 2.95, 3.40 a) Calculate a 95% confidence interval for the population mean GPA. b) If the confidence level is increased from 95% to 99%, will the length of the confidence interval increase, decrease, or remain the same?

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