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Hypothesis calculation

An old scale displays a weight that is uniformly distributed between the real weight ±10 lbs. For example for a person with weight 110 lbs, the scale will show a weight uniformly distributed between 90 and 110.
Consider the null hypothesis that a person weighs 100 lbs, and the alternative hypothesis that the weight is lower.

What is the p value (in percentage) of 91?

What is the p value (in percentage) of 90?

What is the highest weight in lbs for which we can reject the null hypothesis with significance level 10%?


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Answer #1

So the question is somewhat poorly worded. We need to know if the probability distribtuion is continuous or discrete. A scale would typically be limited to discrete values and thus the probability would be limited to the total number of discrete values the scale can display.

If we were to assume that this is a continous distribution then,


What is the p value (in percentage) of 91?

(91-90)/(110-90) = 5%


What is the p value (in percentage) of 90?

(90-90)/(110-90) = 0%


What is the highest weight in lbs for which we can reject the null hypothesis with significance level 10%?

(x-90)/(110-90) = 10%

x =92 lbs


If it were a discrete value say integers only then its a 1/21 chance your weight lands between 90 and 110.


What is the p value (in percentage) of 91?

Probability of 90 and 91% which is 2/21

What is the p value (in percentage) of 90?

Probability of 90 which is 1/21


What is the highest weight in lbs for which we can reject the null hypothesis with significance level 10%?

92 lbs would give a p value over 10%


answered by: Mpw99
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