The test statistic of z = -3.36 is obtained when testing the claim that p < 0.31.a. using a significance level of α = 0.01, find the critical value(s). b. should we reject h0 or should we fail to reject h0?

We can reject the null hypothesis. There is significant evidence that p<0.31 at α = 0.01

Step-by-step explanation:

To test the the claim p < 0.31, null and alternative hypotheses are:

: p=0.31

: p<0.31

For α = 0.01, one tailed test critical value is -2.33

For z=-3.36 , p value is ≈ 0.0004

Since p-value<significance level (0.0004<0.01), we can reject the null hypothesis. There is significant evidence that p<0.31 at α = 0.01

Step-by-step explanation:

Let the first term T1 be a,

second term T2 = a+d where d is the common difference

If the third term and each term thereafter is the average of the two terms immediately preceding it then;

T3 = T2+T1/2

T3 = a+d+a/2

T3 = 2a+d/2

Since the first term of the sequence is 20 and the second term is 8;

a = 20 ... 1

a+d = 8 ... 2

from 2; d = 8-20

d = -12

T3 =  2(20)+(-12)/2

T3 = 40-12/2

T3 = 28/2

T3 = 14 (This value is an integer)

We will proceed to check the fourth term of the sequence.

T4 = T3+T2/2

T4 = 14+8/2

T4 = 22/2

T4 = 11 (This is also an integer)

We will proceed to check the value of fifth term of the sequence.

T5 = T4+T3/2

T4 = 11+14/2

T4 = 25/2

T4 = 12.5 (This is not an integer)

This shows  that the value of the first term in the sequence that is not an integer is 12.5