You may need to use the appropriate appendix table or...

You may need to use the appropriate appendix table or technology to answer this question. In a random sample of 121 observations, p = 0.8. What is the 95% confidence interval for p? 0.64 to 0.96 0.67 to 0.93 0.73 to 0.87 0.74 to 0.86 You may need to use the appropriate appendix table or technology to answer this question. It is known that the population variance equals 522. What is the sample size that needs to be taken if the desired margin of error is 4 or less with 0.95 probability? 501 126 125 502

Transcript

00:01 Let me take notes what's given here.

00:02 There is a sample of 121 observations, so the sample size, which is 121, and the proportion was given as 0 .8.

00:11 And the confidence level was also given here, which is 95%.

00:15 I can write as 0 .95.

00:17 So what i have to do, we need to get the confidence interval.

00:21 So the confidence interval for p, which is the p value, this is plus or minus, the z -alph over to times squared of p times 1 minus p and divided by the sample size here.

00:36 Let me just put all these numbers here, but before we need to get the z alpha over 2.

00:42 So we know that the alpha is equal to 1 minus confidence level.

00:45 So the alpha over 2, which is 1 minus 0 .95 and divided by 2, which would be 0 .025 here.

00:52 And the next step, so the z alpha over 2, which is, so i'm going to use the normal.

00:59 So this is inverse normal function here.

01:03 The area was given 0 .0 .025, the mean for the standard normal distribution and standard division.

01:09 So press second variance.

01:10 The third option here.

01:11 This is 0 .025, 0 and 1.

01:15 So the value is negative 1 .96.

01:18 So i'm going to plug in the numbers here.

01:19 So the confidence interval, which is this is 0 .8 plus or minus 1 .96 times the square of.

01:28 This is 0 .8, 1 minus 0 .8, and divided by the sample size, which is 121.

01:35 Let me get the number.

01:36 First of all, let me take this number and multiply by negative 1 to make it positive, which is 0 .8.

01:42 This is plus the number we got here, and multiply, this is square root of 0 .8 times 0 .2, and this is divided by 121.

01:54 So the upper boundary in this case, let me just write the p.

01:59 Is less than the p hat, which is less than 0 .87...

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