Free Printable Significance Tests

1.

When performing a significance test, we're looking for convincing evidence to __________ the null hypothesis in favor of the alternative hypothesis.

a)

refute

b)

dispute

c)

reject

d)

accept

2.

To answer the question, "Is the evidence convincing enough to reject the null?" we can't just look at our sample statistic. Why not? Because samples ________.

a)

are all the same

b)

vary

c)

are too small

d)

affect the standard deviation

3.

A significance test produces a _______ that accounts for the variability in sampling.

a)

z-score

b)

critical value

c)

t*-value

d)

p-value

4.

Small p-values mean that our sample was very unlikely if the null hypothesis is true. Therefore, small p-values are ________________ that the null hypothesis is wrong.

a)

convincing evidence

b)

believable proof

c)

reliable information

d)

justifiable inference

5.

How small is a small p-value? All year we have defined small as any probability that is less than _________.

a)

1%

b)

2.5%

c)

5%

d)

10%

6.

Whatever probability we choose as the cutoff for what is small is what we call the ____________________.

a)

importance level

b)

significance level

c)

meaningfulness level

d)

insightfulness level

7.

The symbol for the significance level is ____.

a)

$\alpha$

b)

$\theta$

c)

$\pi$

d)

$\mu$

8.

The most common significance levels are _____ ______.

a)

0.1 and 0.5

b)

0.05 and 0.1

c)

0.05 and 0.01

d)

0.5 and 0.01

9.

If p-value < $\alpha$ , then the sample is unusual if the null is correct, so we ______ the null and have convincing evidence that the alternative is true, and the results are ___________.

a)

fail to reject, statistically significant

b)

reject, statistically significant

c)

fail to reject, not statistically significant

d)

reject, not statistically significant

10.

If the p-value > $\alpha$ , then the sample is not unusual if the null is true, so we ______ the null, so there is not convincing evidence that the alternative hypothesis is true, so the results are ________.

a)

fail to reject, not statistically significant

b)

fail to reject, statistically significant

c)

reject, not statistically significant

d)

reject, statistically significant

11.

Lumber companies dry freshly cut wood in kilns before selling it. A certain percentage of boards develop cracks on their ends during drying. The current drying procedure is known to produce cracks in 16% of boards. The drying supervisor wants to try a new method that she believes will result in a proportion of cracked boards that is less than 16%.

Write the appropriate hypotheses.

a)

Ho: p = 0.16

Ha: p = 0.16

b)

Ho: p = 0.16

Ha: p =/= 0.16

c)

Ho: p = 0.16

Ha: p > 0.16

d)

Ho: p = 0.16

Ha: p < 0.16

12.

The drying supervisor uses the new method on a random sample of 200 boards. She conducts a hypothesis test on her sample data and gets a p-value of .027. Based on the p-value , was there convincing evidence that the new method is better? Use $\alpha$ = 0.05.

a)

Since our p-value of 0.027 is < $\alpha$ , we reject the null hypothesis. We have convincing evidence that the new method is better.

b)

Since our p-value of 0.027 is > $\alpha$ , we fail to reject the null hypothesis. We do not have convincing evidence that the new method is better.

13.

Last year, a pineapple company in Hawaii grew pineapples that weighed an average of 31 ounces. The company installed a new irrigation system hoping that this year’s crop of pineapples would be larger than 31 ounces.

Write appropriate hypotheses.

a)

Ho: mu = 31 ounces

Ha: mu > 31 ounces

b)

Ho: mu = 31 ounces

Ha: mu < 31 ounces

c)

Ho: mu = 31 ounces

Ha: mu =/= 31 ounces

d)

Ho: mu = 31 ounces

Ha: mu = 31 ounces

14.

At the end of the current growing season, the quality inspector took a sample of 50 pineapples and conducted a hypothesis test on the sample data. His test produced a p-value of 0.1317. Based on the p-value, was there convincing evidence that the current pineapples are larger? Use $\alpha$ =0.05.

a)

Since our p-value of 0.1317 is < $\alpha$ , we reject the null hypothesis. We have convincing evidence that the pineapples are larger.

b)

Since our p-value of 0.1317 is > $\alpha$ , we fail to reject the null hypothesis. We do not have convincing evidence that the pineapples are larger.

15.

The label on bottles of one company's grapefruit juice say that they contain 180 ml of liquid. Your friend Jerry suspects that the true mean is less than that, so he takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean volume of liquid in the bottles is 179.5 ml and the standard deviation is 1.3 ml. Jerry performs a test of Ho: $\mu$ = 180 ml versus Ha: $\mu$ < 180 ml. The test yields a p-value of 0.0098.

Using a significance level of 1%, is there convincing evidence that there is less than 180 ml of liquid in the bottles?

a)

Since our p-value of 0.0098 is more than $\alpha$ , we reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid.

b)

Since our p-value of 0.0098 is less than $\alpha$ , we reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid.

c)

Since our p-value of 0.0098 is less than $\alpha$ , we fail to reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid.

d)

Since our p-value of 0.0098 is more than $\alpha$ , we fail to reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid.

16.

The EPA has determined that safe drinking water should contain no more than 1.3 mg/L of copper, on average. To test water from a new source, you collect water in small bottles at each of 30 randomly selected locations/ The mean copper content of your bottles is 1.36 mg/L. You perform a test of Ho: $\mu$ = 1.3 mg/L versus Ha: $\mu$ >1.3 mg/L.

The test yields a p-value pf 0.0391. What conclusion would you make for a significance level of 5%?

a)

Since our p-value of 0.0391 is more than 5%, we reject the null hypothesis. We have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

b)

Since our p-value of 0.0391 is more than 5%, we fail to reject the null hypothesis. We do not have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

c)

Since our p-value of 0.0391 is less than 5%, we reject the null hypothesis. We have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

d)

Since our p-value of 0.0391 is less than 5%, we fail to reject the null hypothesis. We do not have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

17.

The EPA has determined that safe drinking water should contain no more than 1.3 mg/L of copper, on average. To test water from a new source, you collect water in small bottles at each of 30 randomly selected locations/ The mean copper content of your bottles is 1.36 mg/L. You perform a test of Ho: $\mu$ = 1.3 mg/L versus Ha: $\mu$ >1.3 mg/L.

The test yields a p-value pf 0.0391. What conclusion would you make for a significance level of 1%?

a)

Since our p-value of 0.0391 is more than 1%, we reject the null hypothesis. We have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

b)

Since our p-value of 0.0391 is more than 1%, we fail to reject the null hypothesis. We do not have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

c)

Since our p-value of 0.0391 is less than 1%, we reject the null hypothesis. We have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

d)

Since our p-value of 0.0391 is less than 1%, we fail to reject the null hypothesis. We do not have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

18.

A Gallup poll report revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders if this result is true for her school. She surveys a random sample of 150 students and 64% of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p=/= 0.72.

The test yields a p-value of 0.0291. What conclusion would you make for a significance level of 5%?

a)

Since our p-value of 0.0291 is more than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

b)

Since our p-value of 0.0291 is less than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

c)

Since our p-value of 0.0291 is more than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

d)

Since our p-value of 0.0291 is less than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

19.

A Gallup poll report revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders if this result is true for her school. She surveys a random sample of 150 students and 64% of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p=/= 0.72.

The test yields a p-value of 0.0291. What conclusion would you make for a significance level of 1%?

a)

Since our p-value of 0.0291 is more than 1%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

b)

Since our p-value of 0.0291 is less than 1%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

c)

Since our p-value of 0.0291 is more than 1%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

d)

Since our p-value of 0.0291 is less than 1%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.

20.

Simon reads a newspaper report claiming that 12% of all adults in the US are left-handed. He wonders if this figure holds true at his college. Simon chooses an SRS of 100 students and 16 of them are left-handed. He performs a test of Ho: p = 0.12 versus Ha: =/= 0.12.

The test yields a p-value of 0.2184. What conclusion would you make for a significance level of $\alpha$ = 0.10?

a)

Since the p-value of 0.2184 > $\alpha$ , we reject the null hypothesis. We have convincing evidence that the proportion of lefties at his college is different from 12%.

b)

Since the p-value of 0.2184 > $\alpha$ , we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of lefties at his college is different from 12%.

c)

Since the p-value of 0.2184 < $\alpha$ , we reject the null hypothesis. We have convincing evidence that the proportion of lefties at his college is different from 12%.

d)

Since the p-value of 0.2184 < $\alpha$ , we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of lefties at his college is different from 12%.

21.

Simon reads a newspaper report claiming that 12% of all adults in the US are left-handed. He wonders if this figure holds true at his college. Simon chooses an SRS of 100 students and 16 of them are left-handed. He performs a test of Ho: p = 0.12 versus Ha: =/= 0.12.

The test yields a p-value of 0.2184. What conclusion would you make for a significance level of $\alpha$ = 0.05?

a)

Since the p-value of 0.2184 > $\alpha$ , we reject the null hypothesis. We have convincing evidence that the proportion of lefties at his college is different from 12%.

b)

Since the p-value of 0.2184 > $\alpha$ , we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of lefties at his college is different from 12%.

c)

Since the p-value of 0.2184 < $\alpha$ , we reject the null hypothesis. We have convincing evidence that the proportion of lefties at his college is different from 12%.

d)

Since the p-value of 0.2184 < $\alpha$ , we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of lefties at his college is different from 12%.

Significance Tests

Total questions: 21

Worksheet time: 11mins

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