Question

Quiz Three Name Directions: Put your answers on the actual quiz where yousee the words PLACEFINAL Staple yourwork to the rear of the stapled quiz and make sure it is organized for analysis of your computations. Lastly, type (or print clearly) and work in which your interpretation is required Dr. Baker believes that virtual reality is one of the biggest technological accomplishments in the 21" century. He creates a statistical program implemented through virtual reality and to testits effectiveness he gives his students a standardized calculus test in weekone of the semester then gives each student a pair of virtual reality googles with his eight week statistical program. He now gives his students another standardized calculus test in week tenof the semester. Did the virtual reality program prove successful at ? .05? 1) He PLACE FINAL ANSWER HERE Week 8 58 Week 1 42 845 50 23 61 50 45 85 90 26 20 35 50 42 48 58 60 PLACE FINAL ANSWERS HERE 77, o 8, at2 .05? 2) what is the confidence interval for ? -218,02-35, at2 : .05? 3) what is the confidence interval for 4) What is the confidence interval for ?-357, ?2-28, at 2-05?

Answer 1

Result:

1).

week1	week2
42	58
45	50
23	61
50	55
45	58
85	90
26	30
20	35
50	42
48	60

Null hypothesis H_o: mu_d = 0 Alternative hypothesis: H_1: mu_d < 0 Lowest tail test t = mu_d/sd/squareroot Rejection Region: Reject Ho if t < -1.8331 Calculated t = -2.7729 falls in the rejection region The null hypothesis is rejected. We conclude that virtual reality program proved successful. Z value at 0.05 level = 1.96 Lower limit = 77-1.96*8 = 61.32 Upper limit = 77 + 1.96 * 8 = 92.68 Lower limit = 218-1.96 * squareroot (35) = 206.4045 Upper limit = 218 + 1.96 * squareroot (35) = 229.5955 Lower limit = 357-1.96 * squareroot (28) = 346.6287 upper limit = 357 + 1.96 *sqrt(28) = 367.3713

Lower tail test

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	10
DBar	-10.5000
Degrees of Freedom	9
SD	11.9745
Standard Error	3.7867
t Test Statistic	-2.7729
Lower-Tail Test
Lower Critical Value	-1.8331
p-Value	0.0108
Reject the null hypothesis

Rejection Region: Reject Ho if t < -1.8331

Calculated t = -2.7729 falls in the rejection region

The null hypothesis is rejected.

We conclude that virtual reality program proved successful.

2).

Z value at 0.05 level = 1.96

Lower limit = 77-1.96*8 =61.32

Upper limit = 77+1.96*8 = 92.68

3).

Lower limit = 218-1.96*sqrt(35) = 206.4045

Upper limit = 218+1.96*sqrt(35) = 229.5955

4).

Lower limit = 357-1.96*sqrt(28) = 346.6287

upper limit = 357+1.96*sqrt(28) = 367.3713