Question

Question 7

In the last question, an insurance company wants to know if the mean area of homes built in 2010 is less than that of homes built in 2009. What is the conclusion at the 0.05 level of significance?

Question 7 options:

There is evidence to conclude that the mean area of homes built in 2010 is less than that of homes built in 2009

There is not enough evidence to conclude that the mean area of homes built in 2010 is less than that of homes built in 2009

There is evidence to conclude that the mean area of homes built in 2010 is not less than that of homes built in 2009

There is not enough evidence to conclude that the mean area of homes built in 2010 is not less than that of homes built in 2009

Question 8

Following are the weights of 5 boxes of cookies, each of which is labeled as containing 16 ounces. Assume that the population of weights is normally distributed.

15.91, 14.21 , 14.88, 16.07, 14.79

A quality control inspector wants to know whether the mean weight is actually less than 16 ounces. Compute the P-value of the test.

Write down your P-value. You will need it for the next question.

Write only a number as your answer. Round to four decimal places (for example: 0.3841).

Question 9

In the last question, an quality control inspector wants to know whether the mean weight of the boxes of cookies is actually less than 16 ounces. What is the conclusion at the 0.05 level of significance?

Question 9 options:

There is evidence to conclude that the mean weight is actually less than 16 ounces.

There is not enough evidence to conclude that the mean weight is actually less than 16 ounces.

There is evidence to conclude that the mean weight is not less than 16 ounces.

There is not enough evidence to conclude that the mean weight is not less than 16 ounces.

Answer 1

Since no data is available for question 7, hence answering only question 8 and 9.

8) To answer the given question, we construct our null and alternative hypothesis as H0: mu = 16 and H1: mu <16, where mu is the unknown population mean weight of the boxes. The test statistic for testing the given hypotheses is

t= (xbar - mu0)/(s/sqrt(n)) ; where xbar = sample mean weight, mu0 = hypothesized value of the population mean, s = sample standard deviation, n = no. of observations in the sample.

We reject H0, if t(observed) < -t(alpha, (n-1)), where t(alpha, (n-1)) is the upper alpha point of a Student's t distribution with n-1 degrees of freedom, or if the p-value is less than the level of significance (alpha).

Here t(observed) = -2.3383 and -t(alpha,(n-1)) = -2.1318 and the p-value = 0.0398 (rounded to 4-decimal place)

9) Since t(observed) < -t(alpha,(n-1)) and p-value = 0.0398 < 0.05 (level of significance, alpha), so we reject H0 and say on the basis of the given sample at 5% level of significance that there is sufficient evidence to conclude that the mean weight is actually less than 16 ounces. (Option (1) is correct).

(The answers are obtained using R-software. Code and output are attached below for verification).