Question

9.Answer with daigrams please. (Extra Credit.) A small sample - the T-distribution) The trees around the Quincy College parking lot have an average length of 4 inches. The leaf lengths are normally distributed, coming from a population with a standard deviation of 0.6 inches. The trees around the Quincy College parking lot are subject to the stimulating aroma of MBTA exhausts. A sample of 20 leaves was taken from these trees and the average leaf length was found to be 4.2 inches. With an α of .01, can we presume that the MBTA exhaust fumes have contributed to the larger leaf lengths?

                  a.         State the null and alternative hypotheses:

                                                H_o:                                                                                                       H₁:

           

                                    b.         What type of test is this (two-tailed, right-tailed, or left-tailed)?

                  c.         Draw a picture of the normal curve representing this test. Shade in the

area(s) meeting the level of significance.

d.         Plot the mean of the sample on the above graph.

                  e.         Can we reject H_o?

                  f.          What is the 99% Confidence Interval in which the true population mean

falls? (A CI problem using t-distribution multipliers.)

10.       The stated average closing costs associated with purchasing a new home in Quincy is

$6,500. A local broker feels that this cost is too low. The broker randomly selects 40 new home sales and finds their average closing cost is $6,600, with a standard deviation of $120. At an α of .05, can we accept the local broker’s premise that the stated average closing cost is too low? (Follow the same steps as you did in the first problem, answering/graphing the answers as appropriate. Use back of the page if you need space.)

Answer 1

This is a simple problem related drawing the hypothesis testing for a a sample .

Before proceeding with the solution we need to keep in mind that here we are provided with population standard deviation and not the sample standard deviation.

Since the sample size is too small, (n=20<30) we can use the population standard deviation as an estimate of the sample standard deviation.

We can show the above inference diagramitcally as shown below

Let us spend some time over process of calculation of the confidence interval of the true mean.

10). Hypothesis testing for one sample vs the population