Statistic T-TEST The melting point of asphalt is critical in areas of the countr
ID: 3152422 • Letter: S
Question
Statistic T-TEST
The melting point of asphalt is critical in areas of the country where the summer-time temperatures cause roads paved with asphalt to become sticky. The surface of regular asphalt will become sticky if the surface temperature exceeds 165F. A new type of asphalt has been developed that is supposed to have a higher melting point. The mean asphalt melting temperatures on 64 stretches of road made from this new asphalt had a mean melting temperature of 172.5F with a standard deviation of 24F. Use this information to answer the questions in this assignment. This problem is a t(63), but use a Z hypothesis test to estimate the t(63).
What is the parameter in this situation?
What is the point estimate for the parameter in this case?
What is the standard error for the point estimator in this case?
What is the set of hypotheses that would be used to test that the mean asphalt melting temperature is 165 versus the alternative that the mean asphalt melting temperature exceeds 165?
What is the value of the test statistic to test the null hypothesis that the mean asphalt melting temperature is 165?
What is the name of the distribution of the test statistic if the mean asphalt melting temperature is really 165? This is the set of values possible for the test statistic when the null hypothesis is true. The specific answer to this question is t(63), but use a Z test to estimate the t(63). Anytime that df>30, Z can be used to estimate t. Either answer, Z or t(63), will receive credit.
What value must the test statistic be more extreme than in order to reject the null hypothesis at the 1% significance level based on the Z distribution?
What is the value of the p-value in this case? Base your answer on Z as an estimate of the t(63), don’t use t(60). Hint: The p-value is the right-tail area associated with the test statistic, that is the area below the negative and the area above the positive.
What is the decision about the null hypothesis in this case with a significance level of 1% if Z is used as an estimate of t(63)? Hint: If the p -value is less than the significance level then reject the null hypothesis. The p-value is the chance that you are wrong if you reject the null hypothesis based on these data.
What is the conclusion about the alternative hypothesis, based on the decision about the null hypothesis? Write a sentence that begins, Conclude, the data do… .
What is the 99% confidence interval to estimate the parameter based on these data?
Does the above confidence interval contain the hypothesized parameter value in this case? Write a sentence about what the confidence interval indicates about the parameter value.
Explanation / Answer
The parameter of interest is the population mean.
The point estimate for the parameter in this case is the sample mean= 172.5F
The standard error for the point estimator in this case is:
SE(M)=sigma/root over n
=24/root over 64
=3
The null hypothesis is H0:mu=165
Against the alternative hypothesis H1:mu>165
The value of test statistic is:
Z=M-mu/ SE(M)
=(172.5-165)/3
=2.5
The P value for z score of 2.5 is: 1-0.9798=0.0202
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