Question

a. all Hypothesis Tests must include all four steps, clearly labeled;

b. all Confidence Intervals must include all output as well as the CI itself

c. include which calculator function you used for each problem.

2. An experiment was done to see whether open-book tests make a difference. A calculus class of 48 students agreed to be randomly assigned by the draw of cards to take a quiz either by open-notes or closed-notes. The quiz consisted of 30 integration problems of varying difficulty. Students were to do as many as possible in 30 minutes. The 24 students taking the exam closed-notes got an average of 15 problems correct with a standard deviation of 2.5. The open-notes crowd got an average of 12.5 correct with a standard deviation of 3.5. Assume that the populations are approximately normal. At the 5% significance level, does this data suggest that differences exist in the mean scores between the two methods?

Answer 1

Given

n1=24 and n2=24

X1bar=15 and X2bar=12.5

S1=2.5 and S2=3.5

Here populations are approximately normal and alpha =0.05

a)Hypothesis Test

Steps of hypothesis testing

1.The null and alternative hypothesis

2. Tail of test

3.Decision

4.Conclusion

To test this type of two-sided hypothesis problem you can be used Ti-84 plus silver edition calculator because you have mentioned in c)

Step 1:

We have to test open book test make a difference or not

that is the null hypothesis and the alternative hypothesis is

H0:- There is no significant difference between the means of closed notes and open notes test

against

Ha:-There is a significant difference between the means of closed notes and open notes test

Step 2:

This is two-tailed tets (Two-sided) Hence

Step 3:-

We have to apply quality of two-sample mean t-test hence we have to use T tets statistics

Command for Ti-84 Calculator to find test statistic value and P-value

Go to STAT-  click on TEST-Press 4 key for choosing 2 sample t-test plug all the values of  

n1=24 and n2=24

X1bar=15 and X2bar=12.5

S1=2.5 and S2=3.5

Click on calculate and write down the result values

Step4:

Decision

Using the classical approach

if calculated t >=tabulated t

then Reject null hypothesis otherwise fail to reject the null hypothesis

Using the P-value approach

if P value<alpha

then Reject null hypothesis otherwise fail to reject the null hypothesis

Here P value=0.06>0.05(alpha)

Hence Fail to reject the null hypothesis

Step 5:

Conclusion

Hence

There is no significant difference between the mean of closed notes and open notes tests. that is an open book test not make a difference.

b)

Confidence Interval

Using Ti-84 Calculator Command

Go to STAT-  click on TEST-Press 0 key for choosing 2 -sample t-interval

plug all the values of  

n1=24 and n2=24

X1bar=15 and X2bar=12.5

S1=2.5 and S2=3.5

Click on calculate and write down the result values and write down the result

The CI is (0.72771,4.2723)

c)

The ti-84 calculator used for this problem and 2-samp T Test and 2-smapTInt

Hence from the above calculation

data does not suggest that differences exist in the mean scores between the two methods