AP STAT Chapters 23-24

Many people believe that playing chess can have a positive effect on reading ability. A sample of n = 8 students was chosen. They participated in a comprehensive chess program, after which they were given a reading test. What is the correct t* for a 95% confidence interval for the true mean reading score?

• a)1.645
• b)2.306
• c)2.365

Tags

CCSS.HSS.IC.B.4

Many people believe that playing chess can have a positive effect on reading ability. A sample of n = 53 students was chosen. They participated in a comprehensive chess program, after which they were given a reading test. What is the correct t* for a 90% confidence interval for the true mean reading score?

• a)1.645
• b)1.671
• c)1.676
• d)2.009

Tags

CCSS.HSS.ID.A.4

9 randomly sampled students were asked how many hours of TV they watched last week. x̅ was 3.5 h and s was 4 h. For 95% confidence and 8 degrees of freedom, t*=2.3. The stem plot was somewhat skewed to the right, with no outliers. What is the 95% conf. int. for m?

• $3.5\pm\left(2.3\right)\left(\frac{4}{\sqrt{3}}\right)$

• $3.5\pm\left(2.3\right)\left(\frac{4}{9}\right)$

• $3.5\pm\left(2.3\right)\left(4\cdot9\right)$

• $3.5\pm\left(2.3\right)\left(\frac{4}{\sqrt{9}}\right)$

A student wanted to assess the average time spent studying for his most recent exam taken in class.  He asked the first 45 students who came to class how much time they spent and recorded the values.  He then used this information to calculate a 95% confidence interval for the mean time spent by all students.  Was this an appropriate use of the t procedure for a confidence interval?

• a)Yes, because we can assume that the time spent studying was normally distributed.
• b)Yes, because the 45 students is a big enough sample to invoke the CLT.
• c)No, because time spent studying is not a quantitative variable.
• d)No, because there was no randomization in choosing the sample.

Tags

CCSS.HSS.IC.B.4

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: μ = 50,000 vs. Ha: μ < 50,000

• b)H0: x̅ = 50,000 vs. Ha: x̅ < 50,000

• c)H0: μ = 50,000 vs. Ha: μ ≠ 50,000

• d)H0: μ = 50,000 vs. Ha: μ > 50,000

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. 

Each of 16 milk cows were fed 2 diets in random order. Milk production was measured for each of the cows while being fed each of the 2 diets so that 32 milk production values were recorded. Matched pairs one-sample t-procedures will be used for inferences. How many degrees of freedom does the applicable t-distribution have? 

• 2
• 8
• 15
• 16

A 99% confidence interval for the mean sugar content (per 5 oz. serving) of a shipment of strawberries is 5.9 to 8.3 grams. What are the values of the point estimate and the margin of error for this confidence interval?

• Point estimate = 5.9; Margin of error = 2.4

• Point estimate = 5.9; Margin of error = 1.2

• Point estimate = 7.1; Margin of error = 2.4

• Point estimate = 7.1; Margin of error = 1.2

• Point estimate = 8.3; Margin of error = 2.4

A 99% confidence interval for the mean sugar content (per 5 oz. serving) of a shipment of strawberries is 5.9 to 8.3 grams. Which one of the following is the best interpretation of the 99% confidence level for the mean sugar content of the shipment?

• There is a 99% probability that the true mean sugar content of the strawberries in the shipment is between 5.9 and 8.3 grams.

• There is a 99% probability that the interval 5.9 to 8.3 has captured the true mean.

• If we constructed many, many confidence intervals from random samples of this size, approximately 99% of the time the true mean would be between 5.9 and 8.3 grams.

• If we constructed many, many confidence intervals from random samples of this size, approximately 99% of the intervals we constructed would capture the true population mean.

• If we constructed many, many confidence intervals from random samples of this size, approximately 99% of the intervals we constructed would capture the sample mean.

A 99% confidence interval for the mean sugar content (per 5 oz. serving) of a shipment of strawberries is 5.9 to 8.3 grams. If we chose to calculate a 95% confidence interval using the same data instead of calculating a 99% confidence interval, which of the following would describe the change in width of the interval?

• It would be wider.

• It would be narrower.

• The margin of error would be the same, but the center of the interval would be different.

• It would have the same margin of error and same center.

• Since the sample mean is a random variable, we cannot predict how the 95% confidence interval would change.