Data for spending is at bottom:

NOTE: SPSS outputs are necessary to show full answer. Please paste all SPSS outputs into the answers.

The researchers conducting the study to examine the effect of income on hardship decision making, are interested in estimating the true population mean of dollars spent per visit to the mall (spending) (check the lab dataset description document on Blackboard for a reference). They collected the data for 120 shoppers at the mall. In the following lab, treat this as a sample.

Open the HardshipDecisions lab dataset in Blackboard Learn or from where you previously saved it.

1. (1 point) Look at the data for spending. What is the sample mean symbol and value (round to 4 decimal places)? State the mean and include your SPSS output in your BBL submission.

2. The researchers want an estimate (or inferred value) for the mean spending and its likely range for the entire population.

a)Estimate the range in which we expect to find the population mean for spending by constructing a confidence interval. This must be done BY HAND. Round to 4 decimal places and show all your work. Assume the population standard deviation is 16. Use a 95% confidence level. Provide the appropriate values on the lines below.

Value at the center of the C.I.: ______________________

Value of the margin of error: ______________________

Confidence interval:(___________, ___________)

b) state as to how you would explain the results from a) to the researchers.

3.The researchers are concerned that the dollars spent per shopper examined in the study is too different from what has been found in other studies. They expected to see an average spending of 84.5 dollars. Based on our data, is there evidence that the true mean spending for the population is significantly different than the expected average of 84.5 at a 5% significance level? Once again, assume the population standard deviation is 16.

a)Perform a hypothesis test BY HAND, completing all the following steps.

i. State your hypotheses.

ii. Calculate the test statistic BY HAND. Round to 2 decimal places and show

your work.

iii.Give the probability statement for the test statistic and the p-value.Round to 4 decimal places and show your work.

b) Draw your conclusions from the test.

c)Based on part b), decide whether the researchers' concerns are warranted. In other words, is there a reason to believe that the dollars spent per visit to the mall is different than previously expected?

4.Can we use the results from #2a to test the hypothesis from #3? If so, explain why and how. If not, explain why not.

SPENDING DATA

65.51

82.75

69.47

95.71

76.53

67.27

77.3

77.21

66.44

41.97

74.25

93.66

42.68

81.66

73.51

64.1

77.04

102.3

109.06

63.58

98.99

86.7

53.3

90.16

54.09

84.18

88.94

77.88

75.67

74.3

68.3

45.77

44.67

130.84

79.74

81.56

80.12

73.07

85.07

81.45

51.41

67.5

79.27

103.48

37.52

99.72

55.1

88.31

74.23

96.82

61.06

65.92

71.83

62.98

61.04

105.58

75.93

101.92

103.68

90.25

105.94

109.36

76.78

116.37

106.04

60.1

85.64

80.28

71.54

65.76

96.39

91.49

101.92

99.79

86.52

50.82

90.6

84.61

102.25

111.32

52.15

100.33

71.9

89.94

109.53

51.09

101.86

100.82

81.36

74.32

50.45

103.48

49.03

100.68

83.56

109

95.9

76.36

118.13

87.75

120.54

111.93

38.6

76.5

72.12

87.44

85.91

57.4

94.8

50.01

82.3

78.14

75.61

75.32

71.32

103.65

89.97

90.79

86.29

61.3