Question

1) In a simple random sample of size 70, there were 35 individuals in the category of interest. It is desired to test H0 : p = 0.52 versus H1 : p < 0.52. Compute the test statistic z. 1) A) 2.37 B) 0.50 C) 0.06 D) -0.33

Answer 1

Here we have given that,

Claim: To check whether the proportion is less than 0.52.

The Hypothesis is

v/s

Now,

n= Total number of individuals = 70

x: number of individuals in the category of interest=35

Now, we estimate the proportion p as

=sample proportion =

Test statistic:

Z-statistics=

   =

= -0.33

we get the Z-statistics is -0.33

that is here option D is correct.

Now we find the P-value

= level of significance= 0.05

P-value= P( Z < Z-statistics) as this is one tailed test as our interest is P < 0.52.

= P(Z< -0.33)

= 0.3707

we get the P-value 0.3707

Decision:

Here, P-value > 0.05

That is here we fail to reject Ho(Null Hypothesis)

Conclusion:

There is not sufficient evidence that the proportion is less than 0.52.