If sample size is 34, sample mean is 10.3 standard dev is 3.1 Hypothesis is Ho e

Question

If sample size is 34,
sample mean is 10.3
standard dev is 3.1
Hypothesis is
Ho equal or less than 9
H1 is greater than 9

98% Confidence Interval for µ is
10.3 ± 2.33 x 0.5316
= (9.0632 , 11.5368)
z-stat is 2.4452

significance level is 0.01

Q1)how do i find the rejection region cut off? using what table andwhat?
Q2)also how do i find the p-value, which is suppose to be 0.0072?someone explain this!





Q3 answer this too if you can)And ALSO give an example of what ifit's Ho = 9 and H1 != 9 with two tails (is there a difference infinding this t value compared to one tail?), how would one find therejection region, and p-value? ALSO, if the confidence interval is98%, how would you find it(SAME STEPS AS ONE TAIL C.I.)?
solution,

98% Confidence Interval for µ is
10.3 ± 2.33 x 0.5316
= (9.0632 , 11.5368)

Hypothesis
H0: µ = 9
H1: µ 9

Tests Z-stat = 1.3 = 2.4452
Statistic 0.5316

Significance Level = 0.01

Rejection Region =
Tail = BOTH
Cutt -Off = Z-alpha/2 = 2.576
Decision = Do NOT Reject H0

p-value = 0.0145

Explanation / Answer

You are doing a t test, andlooking to see if the answer is likely to occur by chance, WHEN YOU GET THE CALCULATED Z SCORE YOU LOOK ON THETABLE TO SEE IF IT IS IN THE MIDDLE OF THE CHART, WHICHMEANS IT IS LIKELY TO OCCUR BY CHANCE. WHEN YOU GET THE CALCULATED Z SCORE YOU LOOK ON THETABLE TO SEE IF IT IS IN THE MIDDLE OF THE CHART, WHICHMEANS IT IS LIKELY TO OCCUR BY CHANCE. if not in the middle,then unlikely to be chance and so you reject the null Ho.If it is in the middle, it is likely to be chance alone, andyou accept Ho. N=34,
x= 10.3
sd=3.1
Hypothesis is
Ho +<9
H1 >9

98% CI for µ is 10.3 ± 2.33 x 0.5316 =(9.0632 , 11.5368)
z-stat = 2.4452

significance level is 0.01

YOUR TEST STATISTIC IS 0.0072. THIS IS FROM THE CHART ONLINE,JUST LOOK AT THE Z TABLE AND THE SCORE OF 2.4452 IS AT .0072. IT ISWAY IN THE TAIL END, VERY UNLIKEY TO GET SUCH A SCORE BYCHANCE, SO YOU REJECT THE NULL HYPOTHESIS. IT IS LESS THAN0.01

A TAIL MEANS YOU HAVE TO LOOK AT BOTH ENDS OF THE DISTRIBUTOIN, YOUCARE ABOUT A VERY HIGH OR VERY LOW EFFECT. IN SOME CASES YOU DONOT, FOR EXAMPLE IF A DRUG RAISES CHOLESTEROL, ITIS INEFFECTIVE, YOU DONT NEED TO USE THAT DRUG, YOU DID NOT PROVEIT WORKED, YOU NEED ONLY A ONE TAIL TEST.

if 98%, YOU PICK A Z SCORE THAT IS NOT SO FAR OUT ON THE TAIL AND YOU ARE MORE LIKELY TO REJECT THE NULLHYPOTHESIS.

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