Question 1068667: Direction: Answer the two questions completely. Show ALL your solutions. Type your answers in an A4 size bond paper.
1. One of your friends knows that you are taking Advanced Placement Statistics and asks for your help wither Chemistry lab report. She has come up with five measurements of the melting point of a compound: 122.4, 121.8, 122.0, 123.0, and 122.3 degrees Celsius.
a. The lab manual asks for a 95% confidence interval estimate for the melting point. Show her how to find this estimate.
b. Explain to your friend in simple language what 95% confidence interval means.
c. Would a 90% confidence interval be narrower or wider than the 95% interval. Explain your answer to your friend.
d. The lab manual asks whether the data show sufficient evidence to call into question the established melting point of 122 degrees Celsius. State the null and alternative hypotheses and find the P-value.
e. Explain the meaning of the specific P-value to your friend.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! You need the mean and sd
Add them and divide by 5 and the mean is 122.3
Take the squared differences from 122.3, add them and divide by (5-1) or 4, and then take the square root of that, or 0.4583.
a 95% CI is t df=4 0.975, which you can take from a table (2.776) and multiply it by the std dev (0.4583) and divide by sqrt(5), the sqrt (sample size). That is the interval width, and it is 0.5690.
The interval is subtracted and added to the mean to get two numbers
(121.7, 122.9)
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What this means is that we do not know the exact melting point of the compound, but we are highly confident that it lies in the above interval. Stated another way, were we to construct 100 intervals from 100 different samples of 5, the true value would lie in 95 intervals, although we would not know which 95.
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90% confidence is narrower, because we are less confident of the answer, therefore it can be in a narrower interval. Take the extreme case of complete confidence. That would require an infinite interval. The higher the confidence, the wider the interval has to be.
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Ho is melting point is 122
Ha is melting point is not 122
alpha is 0.05
the p-value is 0.22, so it is quite likely we could obtain a result of 122.3 with the true mean's being 122. Such would occur about 1 time in 5, and we generally use 0.05 or less as being a result not due to chance.
Also, the value 122 lies within the 95% confidence interval, therefore, we are highly confident the melting point is 122.
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