2.02 Quiz: Working With P-Values and Statistical Significance

Margaret's Sock Emporium sells hand-knit wool socks. Margaret claims the mean amount of wool per pair is 2 oz, with a standard deviation of .2 oz. You take a random sample of 40 socks and find that the mean weight is 1.9 oz. What's the P-value for getting a sample mean of 1.9 oz or less?

.0008

A researcher believes a population of fish has a normal distribution with a mean weight of 3.4 kilograms and a standard deviation of .8 kilograms. She takes a simple random sample of 30 fish and finds that the mean is 3 kilograms. What's the P-value for a sample mean of 3 or less? (Hint: Remember to use the distribution of x with bar on top.)

.0031

In a particular carnival game, there's a 1/36 chance of winning. In a single day, a participant plays 100 rounds, and wins in 7 of them. What's the P-value for winning 7 or more out of 100 rounds? (Hint: Be sure you know which kind of probability distribution you're dealing with before you do the calculation.)

.0217

In a normal sampling distribution with a mean of 0, what's the P-value for z ≥ 1.89?

.0294

A researcher believes the mean for a certain normally distributed population is 102. The standard deviation is known to be 15. What's the P-value of drawing a random sample of 50 and getting a mean of 100 or less? Would this be strong, statistically significant evidence that the population mean is less than 102?

.1727, not strong evidence

Researchers are testing a treatment for tumors. They've found that tumors are shrinking in patients receiving the new treatment. Their calculations suggest that if chance were the only factor, there's a 2% chance they'd get the same results. Using a significance level α of .01, they conclude the results aren't significant. Would the results be more convincing if they'd used an α of .05? Why?

No. Raising the significance level α wouldn't lower the P-value.

Researchers are testing a treatment for tumors. They've found that tumors are shrinking in patients receiving the new treatment. Their calculations suggest that if chance were the only factor, there's a .9% chance they'd get the same results. At a .01 significance level, do the researchers have proof the new treatment is working?

No. They may have one piece of evidence, but they don't have proof.

In a particular carnival game, there's a 1/36 chance of winning. In a single day, a Pedro plays 100 rounds and wins in 7 of them. You think Pedro may be cheating. If you were to test this theory, what would be an acceptable null hypothesis?

Pedro wins about 1 out of every 36 rounds; the wins are due to chance alone.

In a particular carnival game, there's a 1/36 chance of winning. In a single day, Jose plays 100 rounds and wins 7. You think Jose may be cheating. At a significance level of .05, are your results significant, and do you have evidence that Jose may be cheating?

Results are significant and there's evidence that Jose may be cheating.

A researcher thinks a population of fish has a mean weight of 3.4 kilograms and a standard deviation of .8 kilograms. She takes a simple random sample of 30 fish and finds that the mean is 3 kilograms. True or False: Using a significance level of .05, there's significant evidence that the population mean is actually lower than 3.4 kilograms.

True