1) Calculate the margin of error and construct the confidence interval for the population mean (you may assume the population data is normally distributed):

a.x=99.4, n=70,=1.25,=0.1,

E=?

Round to 3 significant digits

? << ?

Round to 2 decimal places

b.x=51.3,n=96,=12.6,=0.05

E=?

Round to 3 significant digits

? <

Round to 2 decimal places

2) A sports reporter conducts a study of the fans' overall satisfaction with the sporting event after the event is completed. He surveys 165 randomly selected fans on their way out of the event and asks them to rate their satisfaction with the event on a scale from 0 to 10. The average satisfaction rating is 6.4. It is known from previous studies of this type that the standard deviation in satisfaction level is 2.8. Calculate the margin of error and construct the 95% confidence interval for the true mean satisfaction level for the sporting event.

E=?

Round to three decimal places if necessary

? <

Round to three decimal places if necessary

3) Calculate the margin of error and construct the confidence interval for the population mean using the Student's t-distribution (you may assume the population data is normally distributed).

a.x=88.6,n=63,s=15.1,x=88.6,n=63,s=15.1,95% confidence

E= ?

Round to two decimal places if necessary

? <

Round to two decimal places if necessary

b.x=31.1,n=44,s=11.3, 90% confidence

E= ?

Round to two decimal places if necessary

?<

Round to two decimal places if necessary

4) A health insurance broker records the monthly extended health and dental insurance premiums for 18 non-smoking white-collar clients between the ages of 31 and 40 (measured in $):

112

49

126

79

123

47

131

98

152

85

55

56

100

122

144

76

81

117

a.Calculate the sample mean and standard deviation.

x=?

Round to the nearest cent

S=?

Round to the nearest cent

b.Construct a 95% confidence interval for the mean monthly insurance premium for all non-smoking white-collar clients between the ages of 31 and 40.

<<=?

Round to the nearest cent