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What is H0 (sign test)

this question is reallly baffling me.

Q. Eight apples are chosen at random from a crate containing a large number of apples. the masses, in grams are:

147, 138, 171, 142, 152, 145, 141, 143

use a sign test at the 5% significance level to test wheather the median mass of the apples is 150 g.
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what is the null hypothesis? is it that the median is Not equal to 150 and the alternative hypothesis is that the median is equal to 150 or vice versa?

i looked at the back of the book and it says p=0.289 which is >0.05, so no significant evidence that the mean is not 150.

where did they get that value of p from? i know i have to use the binomial distribution whith paramtres (8, 0.5) but what value of x?

safe
Reply 1
Null hypothesis H0 is that the median is 150g. And are you sure it's not the mean, rather than the median?
this is a non parametric test it does not consider the mean unlike parametric tests such as z test and t test, so yh its testing the median not the mean

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