Question

A) In a​ one-tail hypothesis test where you reject H 0 only in the lower ​tail, what is the p value if Z STAT = -1.68? Round decimal to four places

B) In a​ one-tail hypothesis test where you reject H0 only in the upper​ tail, what is the critical value of the​ t-test statistic with 48 degrees of freedom at the 0.10 level of​ significance? The critical value of the t-test statistic is____ ? Round 4 decimal places

C) In a random sample of 200 items,12 are defective. If the null hypothesis is that 10% of the items in the population are​ defective, what is the value of Z STAT​? Round 2 decimal places as needed

Answer 1

A) Z stat = -1.68

For lower tail test : P value = P(Z < Z stat)      

For upper tail test: P value = P(Z> Z stat)

For two tail test : P value = 2 * P(Z > |Z stat| )

Given that the hypothesis test is lower tail test.

Hence, P value = P(Z < Z stat)

                         = P(Z< -1.68)

                         = 0.0465    (From statistical table of table of areas to the left of Z)

P value = 0.0465

B) DF = 48, level of significance = 0.1

We can find critical value from statistical table of t values.

From table , Critical value =( 1.301+1.299 )/2 = 1.3       (Here we have to take average because for 48 df t table does not give the exact value. Hence we have to calculate the average of 40 df and 45 df for corresponding alpha = 0.1 for one tail test)

If we want exact p value we can find it from excel using command " = TINV(2*alpha, df) " = 1.2994

The critical value for t test statistic is 1.2994 = 1.3

C) n= 200 , p_hat = Number of defectives/ n = 12/200 = 0.06

Null hypothesis:             Ho : P=0.10   where = 0.1

Alternative hypothesis : H1 : P 0.10

The unbiased estimator for true population proportion is p hat if following conditions are satisfied:

n*Po and n*(1-P0) should be greater than or equal to 5

n*Po = 200*0.1 = 20 and n*(1-Po) = 200*0.9 = 180.     here conditions are satisfied.

Test statistic : Z stat =

where SE(p hat) =

SE (p hat)= 0.02121

Z stat = (0.06-0.1)/0.02121 = -1.8859 = -1.89

The value of Z stat is -1.89