Question 80062: Question 1
A fast food restaurant claims that the mean time is not equal to 3 minutes. A random sample of 45 customers revealed a mean waiting time of 3.3 minutes with a standard deviation of 0.7 minutes. Test the restaurants claim at a, a= 0.05 level of significance. Assume that the population is normally distributed, and the population standard deviation is 0.7. Use the P-value method.
Question 2
A researcher at NYU claims that for Mathematics courses the proportion of grades B or higher was more than 33.0%. In a random sample of 100 grades issued in the year 2006 there were 27 F's, 15 D's, 22 C's, 14 B's, 22 A's. At a=0.10 test the researcher's claim.
Question 3
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. Decide to use the t-test or z-test. If you use the z-test use the P-value method.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A fast food restaurant claims that the mean time is not equal to 3 minutes. A random sample of 45 customers revealed a mean waiting time of 3.3 minutes with a standard deviation of 0.7 minutes. Test the restaurants claim at a, a= 0.05 level of significance. Assume that the population is normally distributed, and the population standard deviation is 0.7. Use the P-value method.
Ho: mu=3 min
Ha: mu is not equal to 3 min
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Critical value : z=+-1.96
z(3.3)=(3.3-3)/[0.7/sqrt45]
=0.3/[0.1043]
=2.87
p-value=2*0.002=0.004
Since p
Conclusion mu is not equal to 3 min.
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Question 2
A researcher at NYU claims that for Mathematics courses the proportion of grades B or higher was more than 33.0%. In a random sample of 100 grades issued in the year 2006 there were 27 F's, 15 D's, 22 C's, 14 B's, 22 A's. At a=0.10 test the researcher's claim.
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Ho: p=0.33
Ha: p>0.33
Critical value for alpha=10%=1.28
p-hat=(36/100)
z(0.36)=(0.36-0.33)/sqrt[(0.33*0.67)/100]
=0.03/0.047
=0.638
p-value of 0.638=0.26
Since p>alpha, Fail to reject Ho
Conclusion: p=0.33%
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Question 3
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. Decide to use the t-test or z-test. If you use the z-test use the P-value method.
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Ho: mu=2.9
Ha: mu < 2.9
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z(3.1)=(3.1-2.9)/[0.8/sqrt31]=0.0359....
p-value of 0.0359=0.014
Since p
Conclusion
mu < 2.9
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Cheers,
Stan H.
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