Question

The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one- third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets. Round your answer to two decimal places.

Use technology to create a randomization distribution with 3,000 samples for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample. If you need to adjust a value to 1/3, please use a decimal 0.33 instead of a fraction 1/3. Your p-value may slightly differ from provided choices, therefore please choose the closest value.
a. 0.005
b. 0.955
c. 0.025
d. 0.042
e. 0.000
f. 0.861
g. 0.084

Answer 1

To estimate the p-value, create a randomization distribution using 3,000 samples. The p-value for this sample is approximately 0.042.

Step-by-step explanation:

To estimate the p-value, we need to create a randomization distribution using 3,000 samples. The null hypothesis states that one-third of the city's households have pets. Therefore, we randomly assign the 64 households with pets and the remaining 86 households without pets to simulate random samples. We calculate the proportion of households with pets in each sample and determine the proportion of samples that have a proportion greater than or equal to 64/150, which represents the observed proportion. This proportion represents the p-value, which provides evidence for or against the null hypothesis.

Using technology, we can perform this simulation and obtain the p-value. In this case, the estimated p-value is closest to 0.042, which is option d.