Round sample mean, standard deviation, z-scores to 3 decimal places. When findin

Question

Round sample mean, standard deviation, z-scores to 3 decimal places. When finding sample size, state your answer as a whole number.

Sample sheet for female heights: 45 females students

68,60,64,67,65,66,62,63,60,63,61,64,65,68,63,62,64,72,62,59,64,68,65,63,65,62,67,66,61,61,68,63,63,63,65,69,68,63,62,66,69,69,63,61,68

State the following for the sample female heights.

(a) Sample size (n) =

(b) Sample mean=

(c) Sample standard deviation (s)=

2. Use the sample to make a point estimate of the mean height of the entire female student body.

3. (a) Construct a 93% confidence interval for the mean height of the entire female student body. (Round to 2 decimal places)

(b) What is the width of this interval? (Round to 2 decimal places)

4. (a) Construct a 99% confidence interval for the mean height of the entire feamle student body. (Round to 2 decimal places)

(b) What is the width of this interval? (Round to 2 decimal places.

5. Review your 93% and 99% confidence intervals above. Which is wider and why?

6. Suppose that next year we again will collect data and will want to estimate the mean height of the entire female student body. The minimum sample size we need to take depends on what confidence level and margin of error we specify.

(a) Determine the minimum sample size needed to be 94% confident that the sample mean we get is within 1/4 inch of the true mean.

(b) Determine the minimum sample size needed to be 94% confident that the sample mean is within 1/2 inch of the true mean.

(c) Determine the minimum sample size needed to be 90% confident that the sample mean is within 1/2 inch of the true mean.

7. Answer the following using your answers from question 7 above.

(a) Which sample size requirement in #7a and #7b is larger and why?

(b) Which sample size requirement in #7b and #7c is larger and why?

Explanation / Answer

1. a. n=45

b. Mean =Sumx/n=64.44

c.

Create the following table.

Step 3: Find the sum of numbers in the last column to get.

(xiX¯)2=383.1111

Step 4: Calculate using the above formula.

=((xiX¯¯¯)2/n1)=(383.1111/451)2.95

2. Point estimate of mean=xbar=64.44

3.a. z score for 93% CI is 1.81 as P(-1.81<z<1.81)=0.93

So E=z*sd/sqrt(n)=1.81*2.95/sqrt(45)=0.796

Hence CI=64.444+/-0.796=(63.648,65.240)

b. Width is 1.592

4.a. z score for 99% is 2.58

E=z*sd/sqrt(n)=1.135

CI=64.444+/-1.135=(63.309,65.579)

b. Width of this intervl is 2.27

data data-mean (data - mean)2 68 3.5556 12.64229136 60 -4.4444 19.75269136 64 -0.4444 0.19749136 67 2.5556 6.53109136 65 0.5556 0.30869136 66 1.5556 2.41989136 62 -2.4444 5.97509136 63 -1.4444 2.08629136 60 -4.4444 19.75269136 63 -1.4444 2.08629136 61 -3.4444 11.86389136 64 -0.4444 0.19749136 65 0.5556 0.30869136 68 3.5556 12.64229136 63 -1.4444 2.08629136 62 -2.4444 5.97509136 64 -0.4444 0.19749136 72 7.5556 57.08709136 62 -2.4444 5.97509136 59 -5.4444 29.64149136 64 -0.4444 0.19749136 68 3.5556 12.64229136 65 0.5556 0.30869136 63 -1.4444 2.08629136 65 0.5556 0.30869136 62 -2.4444 5.97509136 67 2.5556 6.53109136 66 1.5556 2.41989136 61 -3.4444 11.86389136 61 -3.4444 11.86389136 68 3.5556 12.64229136 63 -1.4444 2.08629136 63 -1.4444 2.08629136 63 -1.4444 2.08629136 65 0.5556 0.30869136 69 4.5556 20.75349136 68 3.5556 12.64229136 63 -1.4444 2.08629136 62 -2.4444 5.97509136 66 1.5556 2.41989136 69 4.5556 20.75349136 69 4.5556 20.75349136 63 -1.4444 2.08629136 61 -3.4444 11.86389136 68 3.5556 12.64229136

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