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# True or False Questions & Hypothesis Testing

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1. True or false, and explain:

(a) The p-value of a test equals its observed significance level.

(b) The alternative hypothesis is another way of explaining the results; it says the difference is due to chance.

2. Five hundred draws are made at random with replacement from a box of numbered tickets; 276 are positive. Someone tells you that 50% of the tickets in the box show positive numbers. Do you believe it? Answer yes or no, and explain.

Excel (Hypothesis Testing 1)

A researcher assessed the role of routine walking in physical fitness. In this experiment n=60 pair of subjects were matched for age, gender and weight. However, one member of each pair typically walked to work, whereas the other typically drove. Subjects were given a physical fitness test. Their fitness scores are reported in the attached excel file. The higher the fitness score, the better.
The file contains two variables:
- Fitness score in group 1 (walkers)
- Fitness score in group 2 (drivers)
What should be the researcher conclusion? Write a brief report of paragraph commenting on the conclusion.

Data set

walkers drivers
8 9
17 14
18 10
10 11
15 13
13 9
16 10
15 8
13 7
11 10
12 15
16 10
12 9
8 9
17 14
17 10
13 11
15 10
17 9
14 12
12 8
10 11
15 10
12 16
9 10
16 5
8 11
19 14
17 14
12 11
15 14
16 9
14 7
17 8
10 8
15 10
12 13
17 10
12 14
11 9
17 13
18 10
10 10
16 12
13 11
14 10
13 8
10 5
11 10
13 14
17 9
12 10
8 9
16 14
17 11
10 10
15 12
13 15
14 10
12 9.

##### Solution Summary

The solution provides step-by-step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

##### Solution Preview

1. True or false, and explain:
(a) The p-value of a test equals its observed significance level.
True
Explanation:
A p-value is a measure of how much evidence we have against the null hypothesis. The p-value measures consistency by calculating the probability of observing the results from your sample of data or a sample with results more extreme, assuming the null hypothesis is true.
(b) The alternative hypothesis is another way of explaining the results; it says the difference is due to chance.
False
Explanation:
The alternative hypothesis is the hypothesis that sample observations are influenced by some non-random cause. That is, it says the difference is not due to chance.
2. Five hundred draws are made at random with replacement from a box of numbered tickets; 276 are positive. Someone tells you that 50% of the tickets in the box show positive numbers. Do you believe it? Answer yes or no, and explain.
No
Explanation:
The null hypothesis tested is
H0: The proportion of tickets in the box show ...

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