Question

The world's smallest mammal is the bumblebee bat. The mean weight of 40 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams.
Find a 99.9% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Find a 99% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Find a 95% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Find an 80% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Answer 1

using excel we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.264
Sample Mean	1.659
Sample Size	40
Confidence Level	99.9%
Intermediate Calculations
Standard Error of the Mean	0.041742065
Degrees of Freedom	39
t Value	3.5581
Interval Half Width	0.1485
Confidence Interval
Interval Lower Limit	1.51
Interval Upper Limit	1.81

99.9% confidence interval for the mean weight of all bumblebee bats is 1.51 to 1.81

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.264
Sample Mean	1.659
Sample Size	40
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	0.041742065
Degrees of Freedom	39
t Value	2.7079
Interval Half Width	0.1130
Confidence Interval
Interval Lower Limit	1.55
Interval Upper Limit	1.77

99% confidence interval for the mean weight of all bumblebee bats is 1.55 to 1.77

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.264
Sample Mean	1.659
Sample Size	40
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.041742065
Degrees of Freedom	39
t Value	2.0227
Interval Half Width	0.0844
Confidence Interval
Interval Lower Limit	1.57
Interval Upper Limit	1.74

a 95% confidence interval for the mean weight of all bumblebee bats is 1.57 to 1.74

Data
Sample Standard Deviation	0.264
Sample Mean	1.659
Sample Size	40
Confidence Level	80%
Intermediate Calculations
Standard Error of the Mean	0.041742065
Degrees of Freedom	39
t Value	1.3036
Interval Half Width	0.0544
Confidence Interval
Interval Lower Limit	1.60
Interval Upper Limit	1.71

80% confidence interval for the mean weight of all bumblebee bats 1.60 to 1.71