question 12

The annual earnings(in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to(a) find the samplemean, (b) find the sample standarddeviation, and(c) construct a98% confidence interval for the population mean.

100,118

80,437

77,709

67,970

51,574

68,146

94,142

65,797

78,742

74,366

44,680

86,631

60,806

57,878

54,703

78,642

47,576

98,597

81,039

93,010

63,936

74,253

51,042

61,084

91,828

84,012

79,475

64,093

74,614

56,655

46,803

89,014

75,830

61,358

83,091

(a) Find the sample mean.

x=

(Type an integer or decimal rounded to two decimal places asneeded.)

(b) Find the sample standard deviation.

s=

(Type an integer or decimal rounded to two decimal places asneeded.)

(c) Construct a98% confidence interval for the population mean.

___<<____

question 13

Use the confidence interval to find the margin of error and the sample mean.

(0.248,0.350)

The margin of error is _____

The sample mean is ____

question 14

If all other quantities remain thesame, how does the indicated change affect the minimum sample sizerequirement?

(a) Increase in the level of confidence

(b) Increase in the error tolerance

(c) Increase in the population standard deviation

(a) How does an increase in the level of confidence affect the minimum sample sizerequirement? Choose the correct answer below.

An increase in the level of confidence __________the minimum sample size required.

(b) How does an increase in the error tolerance affect the minimum sample sizerequirement? Choose the correct answer below.

An increase in the error tolerance ____________the minimum sample size required.

(c) How does an increase in the population standard deviation affect the minimum sample sizerequirement? Choose the correct answer below.

An increase in the population standard deviation _______the minimum sample size required

question 15

You are given the sample mean and the population standard deviation. Use this information to construct the90% and95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. Ifconvenient, use technology to construct the confidence intervals.

A random sample of 55 home theater systems has a mean price of $148.00. Assume the population standard deviation is $16.60.

Construct a90% confidence interval for the population mean.

The90% confidence interval is (____,____)

(Round to two decimal places asneeded.)

Construct a95% confidence interval for the population mean.

The95% confidence interval is (____,_____)

(Round to two decimal places asneeded.)

Interpret the results. Choose the correct answer below.

A.

With90% confidence, it can be said that the population mean price lies in the first interval. With95% confidence, it can be said that the population mean price lies in the second interval. The95% confidence interval is wider than the90%.

B.

With90% confidence, it can be said that the population mean price lies in the first interval. With95% confidence, it can be said that the population mean price lies in the second interval. The95% confidence interval is narrower than the90%.

C.

With90% confidence, it can be said that the sample mean price lies in the first interval. With95% confidence, it can be said that the sample mean price lies in the second interval. The95% confidence interval is wider than the90%