Question

Elementary Statistics Written Homework No software output is required for this assignment. Sections 6.1 & 6.3 1. 6.58 Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely than 20% to be the correct choice? a. State hypotheses, and calculate the sample statistic. Ho: All choices ARE equally probable $H_o: p = .2$ $H_a: p > .2$ $H_a$: B is more likely to be the correct choice $frac{90}{400} = .225$ b. Are conditions met for using a Normal distribution for this test? Explain. c. Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate. $frac{.225 - .2}{sqrt{frac{.2 imes (1 - .2)}{400}}} = 1.25$ d. Find the p-value and draw a Normal curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A. p-value: 0.106 e. State the conclusion of the test in context, using nontechnical language. f. Find a 95% confidence interval for the proportion of questions on all AP exams having B as the correct choice using the normal distribution and the formula for standard error. Show your calculations. Sections 6.1 & 6.3 MATH 1342 Page 1 of 2

          Elementary Statistics Written Homework
No software output is required for this assignment.
Sections 6.1 & 6.3
1. 6.58 Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A
random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows that
B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this
provide evidence that B is more likely than 20% to be the correct choice?
a. State hypotheses, and calculate the sample statistic.
Ho: All choices ARE equally probable
$H_o: p = .2$
$H_a: p > .2$
$H_a$: B is more likely to be the correct choice
$frac{90}{400} = .225$
b. Are conditions met for using a Normal distribution for this test? Explain.
c. Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate.
$frac{.225 - .2}{sqrt{frac{.2 	imes (1 - .2)}{400}}} = 1.25$
d. Find the p-value and draw a Normal curve with appropriate shaded region. You may give either a
precise p-value from software or bounds on a p-value from Table A.
p-value: 0.106
e. State the conclusion of the test in context, using nontechnical language.
f. Find a 95% confidence interval for the proportion of questions on all AP exams having B as the correct
choice using the normal distribution and the formula for standard error. Show your calculations.
Sections 6.1 & 6.3
MATH 1342
Page 1 of 2

$Elementary Statistics Written Homework No software output is required for this assignment. Sections 6.1 6.3 1. 6.58 Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely than 20% to be the correct choice? a. State hypotheses, and calculate the sample statistic. Ho: All choices ARE equally probable Ho: p = .2 Ha: p > .2 Ha: B is more likely to be the correct choice frac90400 = .225 b. Are conditions met for using a Normal distribution for this test? Explain. c. Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate. frac.225 - .2sqrtfrac.2 imes (1 - .2)400 = 1.25 d. Find the p-value and draw a Normal curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A. p-value: 0.106 e. State the conclusion of the test in context, using nontechnical language. f. Find a 95% confidence interval for the proportion of questions on all AP exams having B as the correct choice using the normal distribution and the formula for standard error. Show your calculations. Sections 6.1 6.3 MATH 1342 Page 1 of 2$

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