Question 1105774: . For each of the following problems, please provide the requested information.
. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
. (b) Identify the sampling distribution you will us: the standard normal or Student’s t. Explain the rationale for your choice. What is the value of the sample test statistic?
. (c) Find (or estimate) the P − value. Sketch the sampling distribution and show the area corre- sponding to the P − value.
(d) Find the critical value(s).
40. Pizza delivery place claims that they can have a pie in your hand in no more than 30 minutes. A random sample of 14 deliveries gave an mean delivery time of 30 minutes and 40 seconds with a standard deviation s of 5 minutes and 51 seconds. Assume that the delivery times are normally distributed. Based on the sample, is the delivery time is greater than the advertised 30 minutes? Use 0.05 as level of significance.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) Level of significance is 0.05
Ho(null hypothesis): X = 30 minutes
H1(alternative hypothesis): X > 30 minutes
H1 is a strict inequality so we have a right-tailed(because >) test
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(b) sample size 14 < 30, so we use the student t-test
sample mean is 30.67 minutes and sample standard deviation(s) = 5.85 minutes
sample test statistic(t-score) = (30.67 - 30) / (5.85/sqrt(14)) = 0.4285
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(c) a t-score of 0.4285 and degrees of freedom(DF) = 14 - 1 = 13 gives us a p-value of 0.337651
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(d) At a 5% significance level, the critical value for a one tailed test is found from the table of t-scores to be 1.771
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Note the p-value of 0.337651 > 0.05, we accept the null hypothesis
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