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Melody

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Melody  11 Feb 2022
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[quote="ChaoticSlumber"]I need help with the following; I've tried putting them into the calculator several different ways and cant get even close to the answers I'm given. Please help me.

For a "before and after" test, 16 of a sample of 25 people improved their scores on a test after receiving computer-based instruction. For H0 : p = 0.50; H1:p is not equal to 0.50; and a significance level of .05:

A. z = 1.2, fail to reject the null hypothesis.

B. z = 1.4, reject the null hypothesis.

C. z = 1.4, fail to reject the null hypothesis.

D. z = 1.64, reject the null hypothesis.
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I am absolutely no stats expert but I will try to help.

This is a binomial distribution because there are only 2 possibilities, either the score improves or it doesn't. (I am also assuming that trial outcomes are indepentant of one another)
The letters I will use are
n = number of trials = 25
p = probability of success if null hypothesis is true = 0.5
q = 1-p = probability of failure if null hypothesis is true = 0.5
X is the number of successes in the 25 trials = 16

If the null hypothesis is true then the expected mean will be n*p = 25*0.5 = 12.5
You could use a binomial probablility table to answer this question but since the np>=5 and nq>=5 , the normal curve is considered to be a good approximation.
The variance (sigma squared) = npq = 25*0.5*0.5 = 25/4
The standard error (like a standard deviation) sigma = sqrt(25/4) = 5/2 = 2.5
z = (x - np) / sigma
= (16 - 12.5) / 2.5
= 3.5 / 2.5
= 1.4
At 5% significance test and a two tail test, the critical z score is +-1.96
That is, Ho will be rejected if |z| > 1.96
|z| = 1.4 < 1.96 Therefore the null hypothesis is NOT rejected.

Here are 2 web pages that I refered to, I looked at others as well but were the ones I used.
http://www.regentsprep.org/regents/math/algtrig/ATS7/BLesson3.htm
http://www.math.armstrong.edu/statsonline/5/5.3.2.html

The second question is very similar, you can try it yourself.
4 Jan 2014
 #55
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Hi Random,
Your answer to my question was excellent
BUT
"I get it now so the reason why it is 12/2 is beacuse that will give you compounding peroid or n then you substitue in equation. That should solve my problem and the rest is substutue so compounding period is how many (things go into another thing.) So if it was 2 months for 3 years the compounding peroid is 36/2 = 18 and to find r it is r/18 and n is n x the net or compounding period."
This beginning statement of yours doesn't make much sense to me.

We need to do some more questions.
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This is the same question as before except I changed 2 months to 3 months

Jo invested some money is invested at 7.2% per year. It is compounded every 3 months for 8 years.
a) Write 7.2% as a decimal
b) How many lots (nets) of 3 months are there in a year . Use this number to get the next 2 answers. (I'm going to call this the key number)
(if you are not totally sure, just post and tell me what key number you intend to use)
c) r is the interest rate per compounding period Find r (show working)
d) n is the total number of compounding periods. Find n (show working) and put n=
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e) What is the compound interest forumula, (n and r are little letters)
f) Substitute in the values of n and r into the equation.
(you can also simplify the equation as a next step)
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g) If the original amount of money was $5000 what has it grown to? show the substitution into the formula.
h) How much interest has Jo earned? (to the nearest cent)

Answer every question carefully, don't cut corners.
Good luck!
4 Jan 2014