# MATH225 Week 7 Assignment – Conduct a Hypothesis Test for Proportion – P-Value Approach

A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 61 people are unemployed.

The following is the setup for this hypothesis test:

H0:p=0.05

Ha:p<0.05

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

 z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.9 0.029 0.028 0.027 0.027 0.026 0.026 0.025 0.024 0.024 0.023 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.03 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.04 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068

P-value = ?

Question

A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime.

The following is the setup for this hypothesis test:

H0:p = 0.35

Ha:p ≠ 0.35

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

 z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.9 0.029 0.028 0.027 0.027 0.026 0.026 0.025 0.024 0.024 0.023 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.03 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.04 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068

P- Value =?

Question

A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. .

The following is the setup for this hypothesis test:

H0:p=0.12

Ha:p≠0.12

In this example, the p-value was determined to be 0.124.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)

Select the correct answer below:

The decision is to reject the Null Hypothesis.
The conclusion is that there is enough evidence to reject the claim.

The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to reject the claim.

## Question

A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts.

The following is the setup for this hypothesis test:

H0:p=0.65

Ha:p<0.65

In this example, the p-value was determined to be 0.277.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)

Select the correct answer below:

The decision is to reject the Null Hypothesis.
The conclusion is that there is enough evidence to support the claim.

The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.

Question

A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam.

The following is the setup for this hypothesis test:

H0:p=0.80

Ha:p>0.80

In this example, the p-value was determined to be 0.944.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)

Select the correct answer below:

The decision is to reject the Null Hypothesis.
The conclusion is that there is enough evidence to support the claim.

The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.

Question

A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700 people is taken in the city and 150 people indicate they are smokers.

The following is the setup for this hypothesis test:

H0:p=0.20

Ha:p<0.20

In this example, the p-value was determined to be 0.828.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)

Select the correct answer below:

The decision is to reject the Null Hypothesis.
The conclusion is that there is enough evidence to support the claim.

The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.

Question

An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%.

To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle.

The following is the setup for this hypothesis test:

H0:p=0.65

Ha:p>0.65

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

 z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.5 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944 1.6 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954 1.7 0.955 0.956 0.957 0.958 0.959 0.96 0.961 0.962 0.962 0.963 1.8 0.964 0.965 0.966 0.966 0.967 0.968 0.969 0.969 0.97 0.971 1.9 0.971 0.972 0.973 0.973 0.974 0.974 0.975 0.976 0.976 0.977

P-value = ?

Question

A human resources representative claims that the proportion of employees earning more than \$50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than \$50,000.

The following is the setup for this hypothesis test:

H0:p=0.40

Ha:p<0.40

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

 z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.5 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944 1.6 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954 1.7 0.955 0.956 0.957 0.958 0.959 0.96 0.961 0.962 0.962 0.963 1.8 0.964 0.965 0.966 0.966 0.967 0.968 0.969 0.969 0.97 0.971 1.9 0.971 0.972 0.973 0.973 0.974 0.974 0.975 0.976 0.976 0.977 2.0 0.977 0.978 0.978 0.979 0.979 0.98 0.98 0.981 0.981 0.982

P-value=?