# Confidence Intervals Statistics Assuming Unequal Variances Analysis

Assignment 3 & 4: Confidence Intervals and t-tests1.

(3 pts) The standard deviation of the weights of elephants is known to be approximately 15 pounds.

We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves.

Fifty newborn elephants are weighed. The sample mean is 244 pounds.

a. Identify the following:

𝑥̅ = ________

𝜎 = ________

𝑛 = ________

b.

Construct a 95% confidence interval for the population mean weight of newborn elephants.

Please note which equation you are using and show your work (hint: we know that the

population standard deviation is 15).

c.

In your own words, describe what your results mean. In other words, interpret your results.

2) (1 pts) A group of doctors is deciding whether or not to perform an operation. Suppose the null

hypothesis, H0, is: the surgical procedure will go well.

a.

State what the Type I error would be

b.

State what the type II error would be

3) (3 points) Suppose that a recent article stated that the mean time spent in jail by a first-time

convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the

new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The

mean length of time in jail from the survey was three years with a standard deviation of 1.8 years.

Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the

distribution of the jail times is approximately normal.

a.

State the H0 and Ha for the study

b.

Conduct a one sable t-test to obtain a t-value

c.

What are the degrees of freedom? Find the critical t-value from the t-table

d.

Do you reject the H0? Interpret your results

4. (5 pts) A psychologist is examining the influence of an older sibling in the development of social

skills. A sample of 32 three-year-old children is obtained. Half of these children had no siblings

and the others had at least one older sibling who is within 5 years of the child’s age. The

psychologist records a social skills score for each child and obtained the following data:

No Sibling

M = 36

n = 16

SS = 470

Other Sibling

M = 42

n = 16

SS = 508

Do these data indicate that having an older sibling has a significant effect on the development of

social skills?

a) State the hypotheses and indicate if it will be a one tail or two tail test

b) Calculate the degrees of freedom and find the critical t-value from the table

c) Compute the t-statistic (hint break this up into 3 steps). Be sure to write out the

equations used to find the t-statistic.

d) Interpret your obtained t and make a decision about the two groups. State the reason

for why you made the decision you did.

5. (5 pts) A researcher would like to test the effect of a new diet drug on the activity level of

animals. A sample of n = 32 rats is obtained and each rat’s activity level is measured on an

exercise wheel for one hour prior to receiving the drug. Thirty minutes after receiving the drug,

each rat is again tested on the activity wheel. The data show that the rats increased their activity

by an average of MD = 42 revolutions with SS = 4000 after receiving the drug. Do these data

indicate that the drug had a significant effect on activity?

a) State the hypotheses and indicate if it will be a one tail or two tail test

b) Calculate the degrees of freedom and find the critical t-value from the table

c) Compute the t-statistic (hint break this up into 3 steps). Be sure to write out the

equations used to find the t-statistic.

d) What decision should the researcher make?

6.

(3 pts) The data below represents data obtained relating to scores on an evaluation from two

different groups of people.

Group 1

15

19

25

12

15

16

17

19

23

24

32

Group 2

20

13

13

20

29

32

23

20

25

15

30

a) You want to determine whether or not there is a significant difference between the

performance of the two groups. What type of test will you be performing and why?

b) Please transfer the data to an excel or google docs file and run the relevant statistical

analysis (see lecture for details on how to do this). Paste the excel/google doc output onto

this document.

c) Interpret the results. Do you reject or fail to reject the null hypothesis. Note the reasons for

your decision.