Result part (a):

90%: 43.5846 to 46.8154

95%: 43.2562 to 47.1438

99%: 42.5823 to 47.8177

Result part (b):

90%: 43.6341 to 46.7659

95%: 43.3343 to 47.0657

99%: 42.7441 to 47.6559

The confidence intervals using a Student's t distribution are more conservative, because the confidence intervals are a little wider than the confidence intervals using the standard normal distribution.

90%: 43.5846 to 46.8154

95%: 43.2562 to 47.1438

99%: 42.5823 to 47.8177

Result part (b):

90%: 43.6341 to 46.7659

95%: 43.3343 to 47.0657

99%: 42.7441 to 47.6559

The confidence intervals using a Student's t distribution are more conservative, because the confidence intervals are a little wider than the confidence intervals using the standard normal distribution.