Question

(a) Find the P – value for the test statistic z=1.36 for the following null and alternative hypotheses:
H0: The population mean is 9.
Ha
: The population mean is less than 9.
The P – value is
(b) Find the P – value for the test statistic z=1.36 for the following null and alternative hypotheses:
H0
: The population mean is 9.
Ha
: The population mean is not equal to 9.
The P – value is

1. Step-by-step explanation:
we need to look up the p-value in the z-table.
for z = 1.36 we get 0.91309.
this is p(the population mean is less than 9).
left-tailed test (less) : p-value = z-table(1.36)
right-tailed test (larger) : p-value = 1 – z-table(1.36)
two-tailed test (not equal to) :
p-value = 2×minimum(z-table(1.36), 1 – z-table(1.36))
(a) is clearly the left-tailed test.
p-value (as above) = 0.91309
(b) is clearly the two-tailed test.
z-table(1.36) = 0.91309
1 – z-table(1.36) = 1 – 0.91309 = 0.08691
the minimum of these 2 values is 0.08691.
so,
p- value = 2×0.08691 = 0.17382
FYI – in both cases that p- value is not small enough (typically it should be <= 0.05) to drop H0.