Question

Write the null and alternative hypothesis for a two-tailed test for each of the following variables: (10 points)

Student Ht Wt Age (Yrs) Shoe Size Waist Size Pocket
Change
01 64 180 39 07 36 018
02 66 140 31 09 30 125
03 69 130 31 09 25 151
04 63 125 36 07 25 011
05 68 155 24 08 31 151
06 62 129 42 06 32 214
07 63 173 30 08 34 138
08 60 102 26 06 25 067
09 66 180 33 08 30 285
10 66 130 31 09 30 050
11 63 125 32 08 26 032
12 68 145 33 10 28 118
13 75 235 44 12 40 060
14 68 138 43 08 27 050
15 65 165 55 09 30 022
16 64 140 24 07 31 095
17 78 240 40 09 38 109
18 71 163 28 07 32 014
19 68 195 24 10 36 005
20 66 122 33 09 26 170
21 53 115 25 07 25 036
22 71 210 30 10 36 050
23 78 108 23 07 22 075
24 69 126 23 08 24 175
25 77 215 24 12 36 041
26 68 125 23 08 30 036
27 62 105 50 06 24 235
28 69 126 42 09 27 130
29 55 140 42 08 29 014
30 67 145 30 08 30 050

Answer 1

Solution:

We can write the null and alternative hypotheses for a two tailed test for each of the given variables in several ways. Some of the null and alternative hypotheses for a two tailed for each of the variables is given as below:

Hypothesis 1

Null hypothesis: H₀: There is no relationship between height of the student and weight of the student.

Alternative hypothesis: H_a: There is a relationship between height of the student and weight of the student.

H₀: ρ = 0 vs. H_a: ρ ≠ 0

Hypothesis 2

Null hypothesis: H₀: There is no relationship between age of the student and shoe size of the student.

Alternative hypothesis: H_a: There is a relationship between age of the student and shoe size of the student.

H₀: ρ = 0 vs. H_a: ρ ≠ 0

Hypothesis 3

Null hypothesis: H₀: There is no relationship between age of the student and waist size of the student.

Alternative hypothesis: H_a: There is a relationship between age of the student and waist size of the student.

H₀: ρ = 0 vs. H_a: ρ ≠ 0

Hypothesis 4

Null hypothesis: H₀: There is no relationship between age of the student and Pocket change of the student.

Alternative hypothesis: H_a: There is a relationship between age of the student and Pocket change of the student.

H₀: ρ = 0 vs. H_a: ρ ≠ 0

Hypothesis 5

Null hypothesis: H₀: The average height of student is 70 inch.

Alternative hypothesis: H_a: The average height of student is different than 70 inch.

H₀: µ = 70 vs. H_a: µ ≠ 70

Hypothesis 6

Null hypothesis: H₀: The average weight of student is 150 pounds.

Alternative hypothesis: H_a: The average height of student is different than 150 pounds.

H₀: µ = 150 vs. H_a: µ ≠ 150