Question

Open Weight_vs_IQ data.

SETUP: Is it reasonable to assume that the IQ and weight of a person should not be related? Given the data, your job is to check if this assertion is indeed reasonable or not. HINT: Read Lecture 24.

19. What would be the correct Null-Hypothesis?

a. IQ and Weight should not be related.

b. The population averages are equal.

c. The slope of the regression line is equal to zero.

d. None of these

20. The P-value is 0.74. What can be statistically concluded?

a. We reject the Null Hypothesis.

b. We accept the Null Hypothesis.

c. We cannot reject the Null Hypothesis.

d. None of these

21. Write a one-line additional comment.

a. We cannot conclude that IQ and Weight have different averages.

b. We are confident that IQ and Weight are related.

c. We cannot conclude that IQ and Weight are related.

d. None of these

Weight  IQ
88      99
112     103
107     97
112     99
80      100
86      90
103     118
121     79
116     80
82      88
65      82
107     103
100     116
91      112
110     92
113     115
105     100
108     94
90      118
73      106
102     126
99      95
80      119
114     116
90      79
95      92
106     78
86      111
106     80

Answer 1

Solution.

The aim of our problem is to test whether body weight and IQ are related or not i.e. is there any linear relationship between body weight and IQ or not.

So we null hypothesis is always the hypothesis of no difference so

19. Answer is a. Ho : IQ and weight should not be related

20. As we know from the definition of p-value that it is the probability of getting extreme result when Ho is true. Oi in other words p-value provides us the measure in favour of Ho at certain fix value of level of significance. i.e. if p value is greater than .05 or .10 we do not rejecte the null hypothesis.

Here p= 0.74 therefore we do not rejecte the null hypothesis.

Answer is b. We accept the null hypothesis.

21. Since the null hypothesis is accepted we conclude that IQ and body weight are not related. So the answer is

c. We cannot conclude that IQ and weight are related.