1. Response insurance collects data on seat-belt usage among U.S. drivers. Of 2000 drivers 25-34 years old, 25% said that they buckled up, whereas 1658 of 2400 drivers 45-64 years oldsaid that they did.(a) At the 5% significance level, do the data suggest that the population proportion of 45-64years old drivers who buckle up is greater than the population proportion of 25-34 yearsold drivers who buckle up?Step 1: Definition of variableP =P2 =Step 2: Find sample size, number of successes, and sample proportion from data.sample size: nsample size: n, =number of successes: x,number of successes: x,X,sample proportion: , :sample proportion: p,X, +X2 =sample pooled proportion: p,n +n,Step 3:Write the hypothesis statement.H, : P = P2H, : P P2 Step 4: Check the assumptions for two-proportion z-test. Use two-proportion z-test for thisproblem.(1) Are the two samples simple random samples?(2) Are the two samples indepedent samples?(3) Is x, > 5 ?Is x, > 5 ?Is (п, - х,)>5?Is (п, — х,) >5?Step 5: Find the rejection area, critical value(s), test statistic, and p-value. Draw thedistribution curve and label the rejection area, critical value(s), test statistic, and p-value on the curve. Use the z table for finding the critical value and p-value for z-test. You can also use the Excel function "norms.dist" for finding p-value for z-test.(P, – P.)Test statistic: TS = z =VP,(1- P,),11-+n,п,Critical value(s): CV =Rejection area: RA= a =p-value: pv =Step 6: Make a decision to reject Ho or not reject Ho based on both critical value and p-value.Do you reject Ho? (Answer: yes or no)Step 7: Draw a conclusion based on the decision in Step 6, i.e.Do the data suggest that the population proportion of 45-64 years old drivers whobuckleupisgreater than the population proportion of 25-34 years old drivers whobuckle up? (Answer: yes or no)

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Description: 1. Response insurance collects data on seat-belt usage among U.S. drivers. Of 2000 drivers 25-34 years old, 25% said that they buckled up, whereas 1658 of 2400 drivers 45-64 years oldsaid that they did.(a) At the 5% significance level, do the data s

When comparing two population proportions the proportion test is used. The test statistic formula…

Math

Statistics

1. Response insurance collects data on seat-belt usage among U.S. drivers. Of 2 34 years old, 25% said that they buckled up, whereas 1658 of 2400 drivers said that they did. (a) At the 5% significance level, do the data suggest that the population prop years old drivers who buckle up is greater than the population proportion old drivers who buckle up? Step 1: Definition of variable Pi = P2 = Step 2: Find sample size, number of successes, and sample proportion from sample size: n = %3D sample size: n, = %3D number of successes: x, = %3D number of successes: x, = %3D sample proportion: p, == %3D !! X2 sample proportion: ê2 !! X, +x2 sample pooled proportion: ê, %3D п +п, ||

1. Response insurance collects data on seat-belt usage among U.S. drivers. Of 2 34 years old, 25% said that they buckled up, whereas 1658 of 2400 drivers said that they did. (a) At the 5% significance level, do the data suggest that the population prop years old drivers who buckle up is greater than the population proportion old drivers who buckle up? Step 1: Definition of variable Pi = P2 = Step 2: Find sample size, number of successes, and sample proportion from sample size: n = %3D sample size: n, = %3D number of successes: x, = %3D number of successes: x, = %3D sample proportion: p, == %3D !! X2 sample proportion: ê2 !! X, +x2 sample pooled proportion: ê, %3D п +п, ||

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

Topic Video

Question

100%

1. Response insurance collects data on seat-belt usage among U.S. drivers. Of 2000 drivers 25-
34 years old, 25% said that they buckled up, whereas 1658 of 2400 drivers 45-64 years old
said that they did.
(a) At the 5% significance level, do the data suggest that the population proportion of 45-64
years old drivers who buckle up is greater than the population proportion of 25-34 years
old drivers who buckle up?
Step 1: Definition of variable
P =
P2 =
Step 2: Find sample size, number of successes, and sample proportion from data.
sample size: n
sample size: n, =
number of successes: x,
number of successes: x,
X,
sample proportion: , :
sample proportion: p,
X, +X2 =
sample pooled proportion: p,
n +n,
Step 3:
Write the hypothesis statement.
H, : P = P2
H, : P P2

Step 4: Check the assumptions for two-proportion z-test. Use two-proportion z-test for this
problem.
(1) Are the two samples simple random samples?
(2) Are the two samples indepedent samples?
(3) Is x, > 5 ?
Is x, > 5 ?
Is (п, - х,)>5?
Is (п, — х,) >5?
Step 5: Find the rejection area, critical value(s), test statistic, and p-value. Draw the
distribution curve and label the rejection area, critical value(s), test statistic, and p-
value on the curve. Use the z table for finding the critical value and p-value for z-
test. You can also use the Excel function "norms.dist" for finding p-value for z-test.
(P, – P.)
Test statistic: TS = z =
VP,(1- P,),
1
1
-+
n,
п,
Critical value(s): CV =
Rejection area: RA= a =
p-value: pv =
Step 6: Make a decision to reject Ho or not reject Ho based on both critical value and p-
value.
Do you reject Ho? (Answer: yes or no)
Step 7: Draw a conclusion based on the decision in Step 6, i.e.
Do the data suggest that the population proportion of 45-64 years old drivers who
buckle
up
is
greater than the population proportion of 25-34 years old drivers who
buckle up? (Answer: yes or no)

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