Question 696922: May you please help me with these five problems.
1. An official with Bartram paint believe that a new additive for the company’s deluxe paint has reduced the average drying time of the paint. She provides the following evidence. For a sample of 50 applications of the old formula, a mean drying time of 100 minutes was obtained. The sample standard deviation was 25 minutes. For a sample 50 applications of the new formula, the mean drying time was 93 minutes, with a standard deviation of 24 minutes. Do these results support her belief, or is the difference that she has noted merely due to random chance? Let alpha=.05.
2. A researcher wants to estimates, for a large population of employees, the proportion of those who have ever, sought professional help for an emotional or mental problem. Another researcher found the proportion in a similar population to be 0.25. if the present researcher wants to be within 0.04 of the true proportion with 99% confidence, how large of a sample needs to be to drawn?
3. A random sample of 300 blue-collar workers in a certain city reveals that 75% are planning to vote for a particular candidate for mayor. Of a random sample of 200 white-collar workers, 70% state that they are planning to vote for the candidate. Can we conclude that the two groups differ in their preference for mayor (assume alpha=.05)?
4. The mean weight of a sample of 100 persons from the Honolulu Heart Study is 64 kg. If the ideal weight is known to be 60kg, is the group significantly overweight? Assume the standard deviation is 12kg.
5. A radio station conducts a survey to determine what local citizens perceive to be the most pressing national problem. Of 300 adults contacted, 120 say that they consider declining moral standards to be the most serious problem. Construct the 95% confidence interval for the population that holds his opinion.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. An official with Bartram paint believe that a new additive for the company’s deluxe paint has reduced the average drying time of the paint. She provides the following evidence.
For a sample of 50 applications of the old formula, a mean drying time of 100 minutes was obtained. The sample standard deviation was 25 minutes.
For a sample 50 applications of the new formula, the mean drying time was 93 minutes, with a standard deviation of 24 minutes.
Do these results support her belief, or is the difference that she has noted merely due to random chance? Let alpha=.05.
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I ran a 2-Sample Z-Test on Ho: u1-u2, and got the following:
test stat: z = 1.980
p-value = 0.0477
Conclusion: Since the p-value is less than 5%, reject Ho.
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2. A researcher wants to estimates, for a large population of employees, the proportion of those who have ever sought professional help for an emotional or mental problem. Another researcher found the proportion in a similar population to be 0.25. if the present researcher wants to be within 0.04 of the true proportion with 99% confidence, how large of a sample needs to be to drawn?
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n = [z/E]^2*pq
n = [2.5758/0.04]^2 * 0.25*0.75 = 778 when rounded up
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3. A random sample of 300 blue-collar workers in a certain city reveals that 75% are planning to vote for a particular candidate for mayor. Of a random sample of 200 white-collar workers, 70% state that they are planning to vote for the candidate. Can we conclude that the two groups differ in their preference for mayor (assume alpha=.05)?
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Ho: p1-p2 = 0
Ha: p1-p2 # 0 (claim)
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If ran a 2-Prop Z-Test and got the following:
stat test: z = 1.2337
p-value = 0.2173
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Since the p-value is greater than 5%, fail to reject Ho.
The test results support the claim.
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4. The mean weight of a sample of 100 persons from the Honolulu Heart Study is 64 kg. If the ideal weight is known to be 60kg, is the group significantly overweight? Assume the standard deviation is 12kg.
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z(64) = (64-60)/[12/sqrt(100)] = 4/(1.2) = 3.3333
The mean weight of the group is 3 1/3 std's over the mean.
The group is significantly overweight as the z value is greater
than 2 .
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5. A radio station conducts a survey to determine what local citizens perceive to be the most pressing national problem. Of 300 adults contacted, 120 say that they consider declining moral standards to be the most serious problem. Construct the 95% confidence interval for the population that holds his opinion.
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p-hat = 120/300 = 0.4
ME = 1.96*sqrt(0.4*0.6/300) = 0.0554
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95% CI: 0.4-0.0554 < P < 0.4+0.0554
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Cheers,
Stan H.
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