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A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07

0.07
.

If 310
310
are sampled, what is the probability that the sample proportion will be less than 0.04
0.04
? Round your answer to four decimal places.

User Valloric
by
8.3k points

1 Answer

4 votes

Final answer:

The p-value represents the probability of obtaining a sample proportion less than or equal to the observed proportion, assuming that the true proportion is equal to the null hypothesis proportion.

Step-by-step explanation:

The p-value represents the probability of obtaining a sample proportion less than or equal to the observed proportion, assuming that the true proportion is equal to the null hypothesis proportion. In this case, the p-value is the probability that the sample proportion will be less than 0.04, given that the true proportion is 0.07. To calculate this probability, we can use the normal distribution approximation. First, we need to calculate the standard error of the sample proportion:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the true proportion and n is the sample size. Plugging in the values, we get:

Standard Error = sqrt((0.07 * (1 - 0.07)) / 310)

Next, we can use the standard normal distribution to calculate the probability:

P(sample proportion < 0.04) = P(Z < (0.04 - 0.07) / Standard Error)

From the standard normal distribution table or calculator, we can find the corresponding Z-score and calculate the probability.

User Uneeb Meer
by
8.0k points