STAT T-TEST question The production of pasture grass for hay is an important agr
ID: 3152423 • Letter: S
Question
STAT T-TEST question
The production of pasture grass for hay is an important agricultural product. A new type of grass, called Teff Grass is advertised to produce 2 ton of hay per acre on the first cutting. Twenty-five test plots of this new grass resulted in average production of 1.92 ton per acre on the first cutting with a standard deviation of .40 ton. Assume that the production of hay is a normally distributed random variable, which is a necessary assumption with this small sample.
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 hay production is 2 ton per acre against the alternative that it differs from 2 ton?
What is the value of the test statistic to test the null hypothesis that the mean hay production is 2 tons per acre?
What is the name of the distribution of the test statistic if the mean hay production is 2 tons?
What value must the test statistic be more extreme than in order to reject the null hypothesis at the 1% significance level?
What is the value of the p-value in this case? State a range of values, not a specific value. Hint: The p-value is the tail areas 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%? 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. Write a sentence for the answer.
What is the conclusion about the alternative hypothesis, based on the decision above 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= 1.92 ton per acre
The standard error for the point estimator in this case is:
SE(M)=s/root over n
=0.40/root over 25
=0.08
The null hypothesis is H0:mu=2
Against the alternative hypothesis H1:mu2
The value of test statistic is:
t=M-mu/ SE(M)
=(1.92-2)/0.08
=-1
The name of the distribution of the test statistic if the mean hay production is 2 tons is t distribution.
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