Question

Suppose that Ha: ??> 3.5 ????, ?? = 1.0, ? = 9 snakes of a rare species, ?̅ = 4.2 ???? ? ? = 0.01. Assume that the length of the Nevada Desert snakes has a Normal Distribution. Which

∗

of the following analyzes shows the values ?, ? - ????? and the decision

taken from the corresponding Hypothesis Test?

Answer 1

We write the hypothesis as

H0 : ? = 3.5 Vs Ha: ? > 3.5

n = sample size = 9

s = sample standard deviation = 1.0

Formula for test statistics

? = 3.5 , n = 9 , s = 1.0 , ?̅ = 4.2

t = test statistics = 2.1

Our test is right tailed beacuse Ha has > sign

Right tailed test means one tailed test

We use either excel or Ti - 84 or Ti -83 to find the p value

df = degree of freedom = n - 1 = 9 - 1 = 8

Excel function

=TDST( test statistics , df , tail )

test statistics = positive value of test statistics

df = degrees of freedom

Tail : 1 when test is one tailed

Tail : 2 when test is two tailed .

=TDIST(2.1,8,1)

Do not forget to type = sign in excel

Press enter

P value = 0.034468762

Above test using Ti -84 and Ti -83

press " STAT "

select " tests "

Select " T Test "

Select " Stats " from " T test "

?0 = 3.2

?̅ = 4.2

sx = s =1.0

n = 9

We select > ?0 beacuse Ha has > sign in it

Then select " Calculate "

and press "enter "

t = 2.1

p = p value = 0.0344687617

Decision rule

1 ] p value ≤   ?   Then we reject H0

2 ] p value > ?   Then we do not reject H0

p = p value = 0.0344687617 and ? = 0.01

P value > ?   So we Do not reject H0

We Do not reject Ho means we are supporting the hypothesis H0 : ? = 3.5

That means we are rejecting Ha: ? > 3.5

So Conclusion:-

There is Insufficient evidence to support the claim that ? > 3.5

I hope this will help you :)