Keller Math 533 Project Part B

So, we should reject the null hypothesis H0. At a 0.05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.

A researcher predicts that listening to music while solving math problems will make a particular area of the brain more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58. From many previous studies with the same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10. (a) Using the .01 level, what should the researchers conclude? Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answers with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution. (b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).

In 2007, the median single family house price in Elmore County, Alabama was $143,200.  A current random sample of 100 single family houses indicates 39 that are valued at more than $143,200 and 61 that are valued less than $143,200.  The researcher is interested in evidence at the .05 level that the median house price has decreased from the 2007 level.

J.T. lives in a single story house with her two children and boyfriend. The home has two bedrooms. J.T’s family is able to complete their activities of daily living in the house.

For some families, living in a multigenerational household has never been a choice. Yet these families love the way that their households are run. By having grandpa live in the home allows for him to participate in the lives of his grandchildren. This goes vice versa, with the grandchildren growing up with their grandparents, it’s extra support for the family. Living in tighter spaces because of more people in the household can be a burden with family members not getting the space that they need. The resulting solution is the new market for multigenerational households. Renovations and new homes are being established to make it more comfy for families to live together, in which allows the families to be closer with one another. While growing

Sixteen years later, in 2007, the number of home owners had risen to 70%, or almost three quarters of all

Students participating in a drug education program are given a drug awareness test at the beginning of the program.  The mean score for the population of 1,231 students is 61 with a standard deviation of 12.  As program director, you're curious as to how parents of the students perform on a drug awareness test and whether or not they are significantly different from the students.  Selecting a random sample of 50 parents, you administer the test and discover a mean score of 56.

We reject the null hypothesis since the test show that p-value of 0.109 is less than .0.05

One can be statistically confident in the conclusion to reject the null hypothesis H0 by performing calculations to derive the confidence intervals. Using the Excel function NORMSINV and inputting the necessary variables (see highlighted figures below), one can determine both the upper and lower

F= [∑ (ŷi- ȳ) /p] / σ^2 = MSR/MSE = 3.56 with p-value = 0.02 < 0.05; σ^2 = ∑ (Yi - ŷi) ^2 / (n-p-1) = 426.61. The F value is statistically significant. Therefore, we have the sufficient evidences reject the null hypothesis.

31. A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? Determine the p-value.

24) Suppose we test the difference between two proportions at the 0.05 level of significance. If the computed z is -1.07, what is our decision?

Since the population standard deviation is known, we can test the above hypothesis by large sample test (Z-test) as follows:

0.82 which implies that if we rejected the equal means hypothesis, we would be making a type I

Channing House is a retirement centre in Palo Alto, California. The data-set “channing” is taken from Klein and Moeschberger (2003). It consists of the ages (in months) of 462 elderly individuals (97 males and 365 females) who were resident at the retirement centre during the period January 1964 to July 1975 when they died or left the centre, as well as the ages (in months) at which the individuals entered the retirement community. The gender of the individuals (coded: Male=1 and Female=2) is also included in the dataset. The interest for this study lies in the life times of the individuals. Over the time of the study 130 women and 46 men died at Channing House.