A simple random sample of size n = 200 drivers with a valid driver's license is asked if they drive an American-made automobile. Of the 200 drivers surveyed, 106 responded that they drive an American-made automobile. Determi majority of those with a valid driver's license drive an American-made automobile at the x = 0.05 level of significance. OC. Continuous D. Qualitative with two possible outcomes What type of hypothesis test is appropriate to conduct for this research? A. Hypothesis test on a population proportion OB. Hypothesis test on a population mean OC. Hypothesis test on a population standard deviation Determine the null and alternative hypotheses. Ho: P = 0.5 H₁: p > 0.5 (Type integers or decimals. Do not round.) Which distribution should be used for this hypothesis test? O A. The normal distribution because the parameter is a proportion, p, and the model conditions are satisfied. OB. The normal distribution because the parameter is the mean, o is known, and the model conditions are satisfied. OC. The chi-square distribution because the parameter is o or o², and the model conditions are satisfied. O D. The Student's t-distribution because the parameter is the mean, o is not known, and the model conditions are satisfied.

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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Question

A simple random sample of size n = 200 drivers with a valid driver's license is asked if they drive an American-made automobile. Of the 200 drivers surveyed, 106 responded that they drive an American-made automobile. Determine if a
majority of those with a valid driver's license drive an American-made automobile at the α = 0.05 level of significance.
C. Continuous
D. Qualitative with two possible outcomes
What type of hypothesis test is appropriate to conduct for this research?
A. Hypothesis test on a population proportion
B. Hypothesis test on a population mean
C. Hypothesis test on a population standard deviation
Determine the null and alternative hypotheses.
Ho: P
= 0.5
H₁: p > 0.5
(Type integers or decimals. Do not round.)
Which distribution should be used for this hypothesis test?
A. The normal distribution because the parameter is a proportion, p, and the model conditions are satisfied.
B. The normal distribution because the parameter is the mean, o is known, and the model conditions are satisfied.
C. The chi-square distribution because the parameter is o or o², and the model conditions are satisfied.
D. The Student's t-distribution because the parameter is the mean, o is not known, and the model conditions are satisfied.

Expert Solution

Step 1: Proportion testing.

1.What type of variable is :

D. Qualitative with two possible outcomes

2.What type of hypothesis test is appropriate to conduct his research :

A. Hypothesis test on a population proportion

3.Determine the null and alternative hypothesis :

$H subscript 0 space end subscript colon space p equals 0.5 space equals p subscript 0 H subscript 1 space end subscript colon p greater than 0.5$

Normal distribution should be used for this hypothesis test

A.The normal distribution because the parameter is proportion p and the model conditions are satisfied.

Sample proportion $p with overparenthesis on top space equals 106 over 200$ =0.53

The test statistic is

Z= $fraction numerator p with overparenthesis on top minus p subscript 0 over denominator square root of fraction numerator p subscript 0 left parenthesis 1 minus p subscript 0 right parenthesis over denominator n end fraction end root end fraction equals space fraction numerator 0.53 space minus 0.5 over denominator square root of fraction numerator 0.5 asterisk times 0.5 over denominator 200 end fraction end root end fraction equals fraction numerator 0.03 over denominator square root of 0.00125 end root end fraction$

= $fraction numerator 0.03 over denominator 0.0354 end fraction$ = 0.8474

p - value = P(Z>0.8474) = 0.1984

Since p-value > $Error converting from MathML to accessible text.$ $alpha$ (=0.05), null hypothesis is accepted.