STAT 200 FINAL PRACTICE TEST - Colorado Mesa University



STAT 200 FINAL PRACTICE TEST

The purpose of this test is to concentrate on the harder parts and cover things not asked on the in-class exams. There is some probability. The HT’s and CI’s are mixed up so you can test yourself to see if you can recognize the right thing to do.

Suggestions for studying for the final: #1. Make sure you review your in-class tests.

#2. The individual practice tests are good too. #3. These questions are good too. You might consider just reading the questions and describing how you would do the problem and then see if the answer key agrees. In other words, you might to save time by not spending all the time calculating everything. Use [pic]=.05 in each problem that requires a significance level. Also give the p-value and its meaning for each HT. Make sure to give the table numbers (critical values) and the data numbers (test statistics) and the yes/no answer for each HT.

1. A box contains 5 blue marbles and 3 green marbles, 2 marbles are drawn without replacement.

A) What is the probability the second is green?

B) What is the probability the first is green?

C) What is the probability the first is green and the second is blue?

D) What is the probability the first is green given the second is blue?

2. A box contains 5 blue marbles and 3 green marbles, 2 marbles are drawn with replacement.

A) What is the probability the second is green?

B) What is the probability the first is green?

C) What is the probability the first is green and the second is blue?

D) What is the probability the first is green given the second is blue?

E) What is the probability that in 10 draws at least 2 will be green?

F) What is the probability that in 10 draws exactly 2 will be green?

G) What is the mean and standard deviation of the number of blue marbles in 100 draws?

H) What is the probability that in 100 draws there will be at least 60 blues?

3. A company makes light bulbs. Assume any necessary conditions to proceed are satisfied even if they aren’t. The problems have very small sample sizes and probably most tests and confidence intervals are somewhat worthless, but calculations should go quickly.

A) Give a 95% CI for the population variance. A random sample of 4 had life spans of 990, 1010, 900, and 880 hours.

B) How many bulbs must be studied to estimate the mean with a 95% CI to within 10 hours? Assume the population standard deviation is 80.

C) How large a sample is needed to estimate with a 95% CI the percentage of bulbs lasting at least 1000 hours to within 1.5%, if there is no initial guess?

D)Two other company’s bulbs are studied. Can it be shown that the mean lifetimes differ between the 3 companies?

| |Company 1 |Company 2 |Company 3 |

|Number of bulbs studied |4 |3 |3 |

|Lifetimes |990,1010,900,880 |1000,900,1200 |850,800,1000 |

E1)A sample of 20 bulbs had a mean lifetime of 1000 hours and a standard deviation of 80 hours. A sample of 10 bulbs from another company had a mean of 1040 and a standard deviation of 50. Can we show that the other company’s bulbs last longer on average?

E2) A sample of 20 bulbs had a mean lifetime of 1000 hours and a standard deviation of 80 hours. A sample of 10 bulbs from another company had a mean of 1040 and a standard deviation of 50. Can we show a difference between how long the company’s bulbs last longer on average?

F) The power consumptions before and after using the “power saving insert” for 4 bulbs are listed.

| |Bulb 1 |Bulb 2 |Bulb 3 |Bulb 4 |

|Power consumption before |60 |61 |59 |60 |

|Power consumption after |57 |58 |57 |61 |

Can it be shown that the insert raises the variance of the power consumption?

G) How large a sample is needed to estimate with a 95% CI the percentage of bulbs lasting at least 1000 hours to within 1.5%, if there is a good initial guess that it is around 30%?

H1) Can it be show that “power saving insert” (see F) changes the power consumption on average?

H2) Can it be show that “power saving insert” (see F) lowers the power consumption on average?

I1) Can we show using the info in A) that the population standard deviation is not 50 hours?

I2) Can we show using the info in A) that the population standard deviation is more than 50 hours?

J) If the mean lifespan is 1000 hours with a standard deviation of 80 hours, what is the probability that a bulb will last at least 1055 hours?

K) In a sample of 60 bulbs 22 lasted at least 1000 hours. Give a 95% CI for the proportion of all bulbs that will last that long.

L) If the mean lifespan is 1000 hours with a standard deviation of 80 hours, what is the probability that a random sample of 4 bulbs will last at least 900 hours?

M1) Using the info in K) and that another company had a sample of 50 bulbs in which 20 lasted at least 1000 hours, can it be proven that the proportion of bulbs lasting at least 1000 hours is different in this other company?

M2) Using the info in K) and that another company had a sample of 50 bulbs in which 20 lasted at least 1000 hours, can it be proven that the proportion of bulbs lasting at least 1000 hours is higher in this other company?

N) Give a 95% CI for how much the “power saving insert” lowers power consumption. See part F.

O) Give a 95% CI for the difference in proportions of bulbs lasting at least 1000 hours between the two companies using the info in parts K and M.

P) Using the data in part A give a 95% confidence interval for the mean lifetime of all bulbs.

Q1) An engineer in the company claims that exactly1/3 of the bulbs last 1000 hours. Using the info in part K can we show he is wrong?

Q2) A consumer group claims that less than 1/3 of the bulbs last 1000 hours. Using the info in part K can we show the consumer group is wrong?

R1) An engineer in the company claims the light bulbs last on average 1000 hours. A random sample of 4 had life spans of 990, 1010, 900, and 880 hours. Can the engineer be proven wrong?

R2) The company claims the light bulbs last on average at least 1000 hours. A random sample of 4 had life spans of 990, 1010, 900, and 880 hours. Can the company’s claim be proven wrong?

S) Using the information in part E give a 95% CI for the difference in mean life times between the two companies.

T) You should use t in parts E, H, P, R, and S because you only are given (or can calculate the sample standard deviation(s)). In any of these problems what distribution would you use if I had given you the population standard deviation(s)?

4. A certain car is made in four colors (black, white, blue, tan) and was made for three years (2000, 2001, 2002). Can we conclude any relationship between the year and color for these cars? Here is data from a random sample.

| |black |white |blue |tan |

|2000 |25 |35 |10 |10 |

|2001 |60 |60 |16 |24 |

|2002 |32 |30 |11 |7 |

5. Using the data in #4 can we show that for 2000 the distribution was not 35% black, 35% white, 15% blue, and 15% tan?

6. A production manager has compared the dexterity scores from a dexterity test of five assembly line employees with their hourly productivity.

|Person |A |B |C |D |E |

|X=dexterity score |12 |14 |17 |16 |11 |

|Y=units produced per hour |55 |63 |67 |70 |51 |

A) Give a scatterplot

B) Find r

C) Can you conclude that [pic], the population linear correlation coefficient is not 0?

D) Find the line of best fit and graph it on the scatterplot.

E) Give a 95% CI for the units produced per hour for Beavis who has a 14 for his dexterity score.

F) Give a 95% CI for the average number of units produced per hour for all workers who score 14 on their dexterity score.

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