Free Printable AP Stats Lesson 7.1-7.2

Worksheets

AP Stats Lesson 7.1-7.2

Total questions: 27

Worksheet time: 2hrs 56mins

Name

Class

Date

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

We are 95% confident that the interval (150, 350) captures the true average caloric content.

We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

None of these are correct.

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

The t distribution is more accurate than a z distribution.

Clarity ratings for the entire bacth are normally distributed.

The t-distribution will create a narrower interval than z.

The standard deviation for the population is unknown.

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

89.08 < μ < 94.92

87.27 < μ < 96.73

87.29 < μ < 96.71

87.77 < μ < 96.23

Which of the following changes to a study would result in a narrower confidence interval?

increasing the confidence level, increasing the sample size

decreasing the confidence level, decreasing the sample size

increasing the confidence level, decreasing the sample size

decreasing the confidence level, increasing the sample size.

What are the critical t-values for an 80% confidence interval given a sample size of 16?

$\pm1.341$

$\pm1.337$

$\pm1.753$

$\pm1.746$

What are the critical t-values for an 95% confidence interval given a sample size of 4?

$\pm4.541$

$\pm3.747$

$\pm3.182$

$\pm2.776$

What are the critical t-values for an 98% confidence interval given a sample size of 4?

$\pm4.541$

$\pm3.747$

$\pm3.182$

$\pm2.776$

As the sample size (n) increases, the $t$ -distribution starts to look more and more like the...

Normal distribution

Binomial distribution

Poisson distribution

Geometric distribution

$df=$

$n$

$n-1$

$\sqrt{n}$

$\sqrt{n-1}$

10.

Which of the following conditions must be met for it to be appropriate to use $s$ as a substitute for $\sigma$ ? Check all that apply.

$\sigma$ is unknown

$\mu$ is unknown

The sample size is at least 30

The data distribution is approximately normal

11.

True or False:

The larger your confidence interval is, the more sure (higher confidence level) you can be.

True

False

12.

The amount added and subtracted to the statistic.

Margin of Error

Point Estimator

Statistic

Population

13.

A sample of 40 people owned an average of 1.35 apple products. It is known from a previous study that the population standard deviation of apple product ownership is 0.63 products. Construct a 95% confidence interval.

(1.11, 1.58)

(1.15, 1.55)

(1.19, 1.51)

(1.09, 1.61)

14.

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144

We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.

There is a 90% chance that CEOs in the electronics industry have salaries that fall between $139,048 to $154,144

We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

15.

The sample size is too small for a z-distribution

Clarity ratings for the entire bacth are normally distributed.

The t-distribution will create a narrower interval than z.

The standard deviation for the batch is unknown.

16.

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers does not believe this is so. They take a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. What set of hypotheses are they interested in testing?

a) H0: m = 50,000 vs. Ha: m < 50,000

b)H0: x̅ = 50,000 vs. Ha: x̅ < 50,000

c)H0: m = 50,000 vs. Ha: m ≠ 50,000

d)H0: m = 50,000 vs. Ha: m > 50,000

17.

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers does not believe this is so. They took a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. If 0.0100 < P-value < 0.0200, what decision should be made if testing at the a = 0.05 level?

a)Reject H0 and conclude that the tires were not performing as claimed.

b)Reject H0 and conclude that the mean tire life really is 50,000 miles.

c)Do not reject H0 and conclude that the tires were not performing as claimed.

d)Do not reject H0 and conclude that the mean tire life really is 50,000 miles.

18.

Another word for average is

sample

mean

data

numerical data

19.

Which of these is a test of means?

Chi square

t test

Pearson correlation

20.

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

refute

dispute

reject

21.

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

z-score

critical value

t*-value

p-value

22.

The symbol for the significance level is ____.

$\alpha$

$\theta$

$\pi$

$\mu$

23.

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 ___________.

fail to reject, statistically significant

reject, statistically significant

fail to reject, not statistically significant

reject, not statistically significant

24.

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 ________.

fail to reject, not statistically significant

fail to reject, statistically significant

reject, not statistically significant

reject, statistically significant

25.

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.

Ho: p = 0.16

Ha: p = 0.16

Ho: p = 0.16

Ha: p =/= 0.16

Ho: p = 0.16

Ha: p > 0.16

Ho: p = 0.16

Ha: p < 0.16

26.

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.

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

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.

27.

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?

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.

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.

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.

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.

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AP Stats Lesson 7.1-7.2

Total questions: 27

Worksheet time: 2hrs 56mins

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