alpha = 0.5, two tailed distribution please answer all parts for up vote. 1.a.)

Question

alpha = 0.5, two tailed distribution
please answer all parts for up vote.

1.a.) = 50, = 3, X = 55.75, n = 20. i. State the null hypothesis and the alternative hypotheses in symbols The null hypothesis the ii. Compute your test statistic (Zobind if true variance is given, or t(dí)obained if true variance is not given). Circle your final ii. State the corresponding critical value you will use (Zeritical or t(df)cntical if true variance is not given) iv. Write a sentence that states your decision to retain or reject the null, including why you decided to retain or reject the null (compare your obtained test statistic to the critical value). Write a sentence that tells me which 2 possibilities exist, given your decision. v.

Explanation / Answer

i)

Null Hypothesis: Sample Mean is close to population mean

Alternate Hypothesis: Sample mean is different from population mean

ii)

We will use t test as sample standard deviation is given (use z test when population std deviation is given)

Thus,

t = (bar x – u)/(s/sqrt(n))

t = (55.75-50) / (3/sqrt(20)) = 8.57

iii)

For df = 20-1 =19, alpha = 0.5

t= 0.68

iv)

absolute value of t(8.57) > critical value of t(0.68)

Thus, we reject the null hypothesis

v)

Sample mean is different from population mean

Or Sample mean is outliner for population mean

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