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# This stats question is frying my brain. CANT DO IT :( watch

1. An initial sample of size 25 from a Normal population with mean ? and
standard deviation ? = 10 gives ¯X = 54.4. Show that the test-statistic for
testing the null hypothesis H0 : ? = 50 against the two-sided alternative
hypothesis H1 : ? = 50 leads to a p-value less than 0.05.
A further sample of size 75 is then taken from the same population, and it
is proposed to reconsider the same hypothesis using the combined sample
of 100 values.
• What values of the mean of these 100 values will lead to p-value
greater than 0.05 when testing H0 for the combined sample?
• Consider the further sample: determine the values of the sample
mean in this further sample which will make the final p-value greater
than 0.05, and find the probability of obtaining a sample mean for
the further sample in this range.

ANY help at all would be brilliant
2. For first part, what is the distribution of the sample mean Xbar under H0 ?
Do you know which probability to calculate to get the p-value?
3. hey.. im doing the same assignment..
the first part you just need to type it into the excel sheet we were given with you hypothesised mean as 50.. then it automatically gives you a test statistics above 1.96 so a p-value less than 0.05
then for the next 2 questions you use
Xbar +/- 1.96 * standard deviation/sqrt(n)

hope that helps.. and i was wondering if you could help me with this question.. ive managed to to part one but not the other 2

An absent-minded statistician has misplaced the values for the population
means and population standard deviations of the random variables X1, X2
and X3. However, she can remember that
Pr {X1 < 40} = Pr {X1 > 80} = 0.025
Pr {X2 < 60} = 0.5, Pr {60 < X2 < 80} = 0.4
Pr {X3 < 30} = Pr {X3 > 70} , Pr {50 < X3 < 65} = 0.4
Use this information to ?nd the values of the means and standard deviations.
4. For part 2: Pr {X2 < 60} = 0.5 obviously tells you something!
Can you find the std dev given that you know the mean and a probability?
5. ive thought that meant that the mean would be 60 but then it make standard deviation 0.. and thats not right when you check it with the other probability
6. oh wait i think i have just worked that out.. i just make an error
7. (Original post by scooby555777)
ive thought that meant that the mean would be 60 but then it make standard deviation 0.. and thats not right when you check it with the other probability
Pr {60 < X2 < 80} = 0.4 ...do you know how to standardise with mean 60 and std dev unknown?

Alternatively: given that 50% of the distribution is less than 60, and 40% is between 60 and 80, you could work with Pr(X2>80)=0.1
8. thankyou for your help ive managed to do part two now.. and i think ive done part 3..

THANKYOU

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