Trials in an experiment with a polygraph include 97 results that include 22 cases of wrong results and 75 cases of correct results. Use a 0.05 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution. Question content area bottom Part 1 Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: p=0.20 H1: p>0.20 B. H0: p=0.20 H1: p<0.20 C. H0: p=0.80 H1: p>0.80 D. H0: p=0.80 H1: p<0.80 E. H0: p=0.80 H1: p≠0.80 F. H0: p=0.20 H1: p≠0.20 Part 2 The test statistic is z=enter your response here. (Round to two decimal places as needed.) Part 3 The P-value is enter your response here. (Round to four decimal places as needed.) Part 4 Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. ▼ Reject Fail to reject H0. There ▼ is is not sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 30PPS

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Question content area bottom

Part 1

Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below.

H0:

p=0.20

H1:

p>0.20

H0:

p=0.20

H1:

p<0.20

H0:

p=0.80

H1:

p>0.80

H0:

p=0.80

H1:

p<0.80

H0:

p=0.80

H1:

p≠0.80

H0:

p=0.20

H1:

p≠0.20

Part 2

The test statistic is

z=enter your response here.

(Round to two decimal places as needed.)

Part 3

The P-value is

enter your response here.

(Round to four decimal places as needed.)

Part 4

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

▼

Reject

Fail to reject

H0.

There

▼

is not

sufficient evidence to support the claim that the polygraph results are correct less than

80%

of the time.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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