Question

An operational hypothesis H₀is that we have a normal process with mean and standard deviation. We wish to test whether or not data (given in cell A1:A100) comes from this process. We will have three different tests. where, mean: -4.48, std dev: 4.86, average: -3.84

Test 1:

What is the lower and upper bound for symmetric 90% confidence interval of average?

Is data average in this confidence interval?

Test 2:

What is the upper bound for 90% one-sided left confidence interval of average?

is data average in this confidence interval?

Test 3:

What is the lower bound for 90% one-sided right confidence interval of average?

Is data average in this confidence interval?

Data of cell (A1:A100​)

-5.12

4.36

-11.22

-10.53

-2.08

-3.01

7.08

-7.08

5.15

-13.38

-5.36

-1.82

-7.31

-5.00

2.59

-0.78

-10.69

-4.56

-3.19

-2.38

-2.47

-11.25

-1.42

-8.21

-6.37

-5.75

-2.28

-15.10

-8.17

-8.64

-8.69

-4.77

-0.11

-3.35

-0.80

-0.99

-1.98

-0.85

-0.73

-7.58

-4.51

-10.72

-6.65

-2.58

-2.26

-6.43

-4.67

-4.44

1.99

-9.24

-11.79

1.73

-5.46

-4.81

-3.71

-0.51

-9.82

6.64

3.81

0.95

-8.91

-5.88

-0.79

3.00

-10.75

-2.93

-1.81

6.70

-4.03

1.09

3.43

-9.72

-10.16

4.95

-7.71

-12.56

-1.59

-1.24

2.93

0.61

-3.87

-4.54

-4.00

-7.77

-11.33

1.32

-5.84

-5.75

3.68

-13.33

1.35

-3.02

-9.45

-0.83

-3.42

-9.57

2.48

-6.74

2.26

-4.02

Answer 1

Sample Size, n= 100

Sample mean, = -3.84

Population standard deviation, = 4.86

Test 1:

At = 0.10, the critical value of a two sided test, = 1.645

90% confidence interval:

Yes, the data average is in this confidence interval.

Test 2:

At = 0.10, the critical value of a left sided test, = -1.28

90% confidence interval for left sided test:

Test 3:

At = 0.10, the critical value of a right sided test, = +1.28

90% confidence interval for right sided test: