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

with two tails means that the chance of rejections isSPLIT INTO TWO PARTS, LEFT and RIGHT, high and low, and when youlook at the Z score it can be VERY POSITIVE OR VERY NEGATIVE. You need to pick the Z score that is critical for yourdecision before you calculate the Z score from you date, then forexample you choose a one tail or two tail test... Z=1.64 is a one tail test at 5%, if Z is >1.64 you rejectnull Z=1.96 is a two tail test at 5%, if X is >1.96 OR <-1.96you reject null H

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