Question

What is the P- Value that corresponds to the given standard score and determine wether to reject the null hypothesis at the 0.05 significance level. Is the alternative hypothesis supported?

z = -3.4 for H0: u = 26 cm and HA: u < 26cm

Answer 1

our hypothesis is left tailed test because H_A has < sign

We have given Z = -3.4

We write Z up to two decimal place

Z = -3.40

We use z table to find the p value

P value = area to the left side of -3.40

Z table directly gives you the left side area.

We look for row headed -3.4 and column headed .00 because -3.40 = -3.4 - 0.00

P value = area to the left side of -3.40 = 0.0003

P value = 0.0003

Decision rule

We have

p value = 0.0003

p value < 0.05 so we reject null hypothesis.

0.0003 < 0.05   so we reject Null hypothesis

Final Answer :-

p value = 0.0003

we reject Null hypothesis