## (CORRECT ANSWER) MATH225N Week 7 Assignment : Conduct a Hypothesis Test for Proportion-p-Value Approach.

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**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%)

Ans:

**Question**

A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000 people are checked and 170 are determined to have the cancer.

The following is the setup for this hypothesis test:

H0:p=0.05

Ha: p<0.05

In this example, the p-value was determined to be 0.015.

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 people who are right-handed is 70%. To test this claim, a random sample of 600 people is taken and its determined that 397 people are right handed.

The following is the setup for this hypothesis test:

*H*0:*p *= 0.70

*Ha *:*p* ≠ 0.70

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 | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |

-2.2 | 0.014 | 0.014 | 0.013 | 0.013 | 0.013 | 0.012 | 0.012 | 0.012 | 0.011 | 0.011 |

-2.1 | 0.018 | 0.017 | 0.017 | 0.017 | 0.016 | 0.016 | 0.015 | 0.015 | 0.015 | 0.014 |

-2.0 | 0.023 | 0.022 | 0.022 | 0.021 | 0.021 | 0.020 | 0.020 | 0.019 | 0.019 | 0.018 |

-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 | 0.030 | 0.029 |

-1.7 | 0.045 | 0.044 | 0.043 | 0.042 | 0.041 | 0.040 | 0.039 | 0.038 | 0.038 | 0.037 |

Provide your answer below:

**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:

*H*0:*p*=0.80

*Ha *:*p*>0.80

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:

Ans:

**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%)

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 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.

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 college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors.

The following is the setup for this hypothesis test:

*H*0:*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 | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |

2.6 | 0.995 | 0.995 | 0.996 | 0.996 | 0.996 | 0.996 | 0.996 | 0.996 | 0.996 | 0.996 |

2.7 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 | 0.997 |

2.8 | 0.997 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 |

2.9 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.999 | 0.999 | 0.999 |

3.0 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

3.1 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

Provide your answer below:

p – Value =

**Question**

A college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and it’s determined that 190 are nursing majors.

The following is the setup for this hypothesis test:

H0:p=0.40

Ha:p>0.40

In this example, the p-value was determined to be 0.001.

Ans.

**Question**

A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149 are nursing majors.

The following is the setup for this hypothesis test:

H0:p=0.40

Ha:p<0.40

The p-value for this hypothesis test is 0.131. Based on this p-value result, interprets the results and come to a conclusion for this hypothesis test for a proportion. Use a significance level of 5%.

Ans:

** ****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:

*H*0:*p* = 0.35

*Ha*:*p* ≠ 0.35

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

z | 0.00 | 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 | 0.030 | 0.029 |

-1.7 | 0.045 | 0.044 | 0.043 | 0.042 | 0.041 | 0.040 | 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 |

Ans.

**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:

*H*0:*p* = 0.35

*Ha*:*p* ≠ 0.35

In this example, the p-value was determined to be 0.075

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 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:

*H*0:*p*=0.40

*Ha*:*p*<0.40

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

**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.

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 business owner claims that the proportion of online orders is greater than 75%. To test this claim, the owner checks the next 1,000 orders and determines that 745 orders are online orders.

The following is the setup for this hypothesis test:

H0:p=0.75

Ha:p>0.75

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

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

z |
0.00 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |

-0.7 |
0.242 | 0.239 | 0.236 | 0.233 | 0.230 | 0.227 | 0.224 | 0.221 | 0.218 | 0.215 |

-0.6 |
0.274 | 0.271 | 0.268 | 0.264 | 0.261 | 0.258 | 0.255 | 0.251 | 0.248 | 0.245 |

-0.5 |
0.309 | 0.305 | 0.302 | 0.298 | 0.295 | 0.291 | 0.288 | 0.284 | 0.281 | 0.278 |

-0.4 |
0.345 | 0.341 | 0.337 | 0.334 | 0.330 | 0.326 | 0.323 | 0.319 | 0.316 | 0.312 |

-0.3 |
0.382 | 0.378 | 0.374 | 0.371 | 0.367 | 0.363 | 0.359 | 0.357 | 0.352 | 0.348 |

-0.2 |
0.421 | 0.417 | 0.413 | 0.409 | 0.405 | 0.401 | 0.397 | 0.394 | 0.390 | 0.386 |

Provide your answer below:

**Question**

A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250 orders and determines that 60 orders are take out orders.

The following is the setup for this hypothesis test:

*H*0:*p*=0.25

*Ha*:*p*>0.25

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

z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |

-0.7 | 0.242 | 0.239 | 0.236 | 0.233 | 0.230 | 0.227 | 0.224 | 0.221 | 0.218 | 0.215 |

-0.6 | 0.274 | 0.271 | 0.268 | 0.264 | 0.261 | 0.258 | 0.255 | 0.251 | 0.248 | 0.245 |

-0.5 | 0.309 | 0.305 | 0.302 | 0.298 | 0.295 | 0.291 | 0.288 | 0.284 | 0.281 | 0.278 |

-0.4 | 0.345 | 0.341 | 0.337 | 0.334 | 0.330 | 0.326 | 0.323 | 0.319 | 0.316 | 0.312 |

-0.3 | 0.382 | 0.378 | 0.374 | 0.371 | 0.367 | 0.363 | 0.359 | 0.357 | 0.352 | 0.348 |

-0.2 | 0.421 | 0.417 | 0.413 | 0.409 | 0.405 | 0.401 | 0.397 | 0.394 | 0.390 | 0.386 |

Provide your answer below:

Ans.

**Question**

A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250 orders and determines that 60 orders are take out orders.

The following is the setup for this hypothesis test:

H0:p=0.25

Ha:p>0.25

In this example, the p-value was determined to be 0.643.

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.

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