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name Punditsdkoslkdosdkoskdo

questions week 7 assignment

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

Here are the steps needed to calculate the p-value for a hypothesis test for a proportion:

  1. Determine if the hypothesis test is left tailed, right tailed, or two tailed.
  2. Compute the value of the test statistic.
  3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0
    If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0
    If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve

 

For this example, the test is a right tailed test and the test statistic, rounding to two decimal places, is:

 

z=0.745−0.750.75(1−0.75)1000−−−−−−−−−−−−√≈−0.37

Thus the p-value is the area under the Standard Normal curve to the right of a z-score of −0.37.

 

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

 

From a lookup table of the area under the Standard Normal curve, the corresponding area is then 1−0.357=0.643.

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