Question

Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions.

Region I:   
386 500 648 767 700 474 1079 684 843 529 745 714

Region II:     ;
707 701 604 824 754 937 730 826 894 1007 714 1021 967 742 608 484

Let be the population mean and be the population standard deviation for . Let be the population mean and be the population standard deviation for . Determine and examine the 90% confidence interval for . Does the interval consist of numbers that are all positive? all negative? or different signs? At the 90% level of confidence, is one region more interesting that the other from a geochemical perspective?

A	The interval contains only positive numbers. We cannot say at the required confidence level that one region is more interesting than the other.

B	The interval contains only positive numbers. We can say at the required confidence level that one region is more interesting than the other.

C	The interval contains both positive and negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.

D	The interval contains both positive and negative numbers. We can say at the required confidence level that one region is more interesting than the other.

E	The interval contains only negative numbers. We can say at the required confidence level that one region is more interesting than the other.

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Question 91 pts

Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions. Let be the population mean for and be the population mean for . Suppose the confidence interval for for a specific level of confidence is - 30.77 to 2.25. Does the interval consist of numbers that are all positive? all negative? or different signs? At the given level of confidence, is one region more interesting than the other from a geochemical perspective?

A	The interval contains only positive numbers. We can say at the required confidence level that one region is more interesting than the other.

B	The interval contains both positive and negative numbers. We can say at the required confidence level that one region is more interesting than the other.

C	The interval contains both positive and negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.

D	The interval contains only negative numbers. We can say at the required confidence level that one region is more interesting than the other.

E	The interval contains only positive numbers. We cannot say at the required confidence level that one region is more interesting than the other.

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Question 101 pts

Suppose a random sample of 347 married couples found that 197 had two or more personality preferences in common. In another random sample of 535 married couples, it was found that only 39 had no preferences in common. Let be the population proportion of all married couples who have two or more personality preferences in common. Let be the population proportion of all married couples who have no personality preferences in common. Find a 80% confidence interval for

A	0.462 to 0.528

B	0.458 to 0.532

C	0.444 to 0.546

D	0.453 to 0.537

E	0.493 to 0.497

Answer 1

$\text{Confidence interval =}\left (\mu_1-\mu_2 \right )\pm t \times SE$

$\text{Where SE is the standard error obtained using the formula, } SE=s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$ $\text{Where } s_p \ \text{is the pooled standard deviation,}\ sp=\sqrt{\frac{\left ( n_1-1 \right )s_1^2+\left ( n_2-1 \right )s_3^2}{n_1+n_2-2}}$

$sp=\sqrt{\frac{\left ( 12-1 \right )187^2+\left ( 16-1 \right )154^2}{12+16-2}}=\sqrt{28476.88}$

$SE=s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_3}}=168.751\times\sqrt{\frac{1}{12}+\frac{1}{16}}=64.4$

$\text{80\% Confidence interval =}\left (\mu_1-\mu_2 \right )\pm t \times SE=111\pm 1.71 \times 64.44$

$\text{80\% Confidence interval =} \left [ 1.09, 220.91 \right ]$

Correct answer: Option B : The interval contains only positive numbers. We can say at the required confidence level that one region is more interesting than the other.

The confidence interval is,

$\text{ Confidence interval =} \left [ - 30.77 ,2.25 \right ]$

Correct answer: Option C) The interval contains both positive and negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.

Correct Answer: Option B) 0.458 to 0.532