Compare confidence intervals

Question

Discuss the below:

Q: Most computer laptops use a rechargeable lithium-ion battery. However, with brighter computer displays and more powerful chips, batteries are not lasting any longer than they did on older computer laptop models.To determine the average number of hours of use that college student gets on a laptop before the batteries fail, 70students were randomly selected, and values of the variable LaptopBatteryLife were recorded.

The variable LaptopBatteryLife is defined as the number of hours that a laptop computer will function.

a. The population standard deviation is believed to be 0.8 hours. Now what is the 95% confidence interval for the mean lifetime? Interpret it. What is the margin of error in this confidence interval? Calculate it using information from the output table

b. The population standard deviation is believed to be 0.8 hours. What is the 80% confidence interval for the mean lifetime? Interpret it.
What is the margin of error in this confidence interval? Calculate it using information from the output table

c. Compare confidence intervals from problem a and b. Which is wider?

d. Determine a 95% confidence interval for the mean battery lifetime assuming the population standard deviation is not known. Interpret it.
What is the margin of error in this confidence interval?

e. Determine a80% confidence interval for the mean battery lifetime assuming the population standard deviation is not known. Interpret it.
What is the margin of error in this confidence interval?

f. Compare confidence intervals from problem d and e. Which is wider?

2.70
1.72
3.24
4.28
4.20
4.73
0.82
2.77
4.10
1.91
2.31
1.31
1.15
2.02
2.23
0.88
2.43
2.60
3.13
2.63
2.67
2.63
4.34
2.91
2.81
2.49
4.97
3.87
5.38
2.35
4.66
1.39
3.54
3.90
4.92
2.92
2.48
3.68
2.62
3.76
1.56
2.15
1.48
2.64
2.97
3.03
2.68
5.19
1.26
2.26
0.42
3.78
2.98
4.15
2.56
3.55
1.89
2.98
3.09
1.78
2.15
1.48
4.67
4.02
3.66
2.95
2.15
3.56
2.89
2.15