Question

Example Problem: [Ch 9, Q36] Consider the following hypothesis test: ?0: ? ≥ 0.75; ??: ? < 0.75. A sample of 300 items was selected. Using ? = 0.05, conduct a hypothesis test and state your conclusions for the following scenarios: ?̅ = 0.68; ?̅ = 0.72; ?̅ = 0.70; ?̅ = 0.77.

Answer 1

Here we have given that,

Claim: To check whether the population proportion is less than 0.75.

The Hypothesis is

v/s

Now,

n=number of items=300

(A)

= sample proportion = 0.68

Test statistic:

= -2.80

Now we find the P-vaue

= level of significance= 0.05

This is left one tailed test

P-value = 0.0026 using z standard normal table

we get P-value =0.0026

Decision:

Here P-value < 0.05

That is here we reject Ho(Null Hypothesis)

Conclusion:

That is There is Sufficient evidence that the population proportion is less than 0.75

(B)

= sample proportion = 0.72

Test statistic:

= -1.20

Now we find the P-vaue

= level of significance= 0.05

This is left one tailed test

P-value =0.1151 using z standard normal table

we get P-value =0.1151

Decision:

Here P-value > 0.05

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

Conclusion:

That is There is Not Sufficient evidence that the population proportion is less than 0.75

(C)

= sample proportion = 0.70

Test statistic:

= -2.00

Now we find the P-vaue

= level of significance= 0.05

This is left one tailed test

P-value =0.0228 using z standard normal table

we get P-value =0.0228

Decision:

Here P-value < 0.05

That is here we reject Ho(Null Hypothesis)

Conclusion:

That is There is Sufficient evidence that the population proportion is less than 0.75

(D)

= sample proportion = 0.77

Test statistic:

= 0.80

Now we find the P-vaue

= level of significance= 0.05

This is left one tailed test

P-value =0.7881 using z standard normal table

we get P-value =0.7881

Decision:

Here P-value > 0.05

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

Conclusion:

That is There is Not Sufficient evidence that the population proportion is less than 0.75