STP226 NAME:



STP 226 FALL 2011

Instructor:

EXAM #2

Material from chapters 5-8

PRINTED NAME: ___________________________________________________

CLASS TIME:______________________________________

Honor Statement:

I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.

Signed ___________________________________

Date_________________________

DIRECTIONS:

This is a closed book examination. You may use an 8x11 page with hand written notes (one side only) and a graphing calculator.

Formulas , z-tables and t-tables are included at the end of the test.

There are 8 problems. You can earn 104 points (4 points are extra credit points ).

For Question #1 there is no need to show work. For remaining 7 problems provide complete and well-organized answers. Include sketches as requested to explain your answers. Round up all answers to at least 4 decimal places.

If you use a calculator for any of the procedures (like computing confidence interval or finding areas under normal or t curves), clearly indicate what calculator and what procedure you used and what specific values you typed in.

Show your work!

RELAX and Good Luck!

Question #1 (2 points each )

Decide if each of the following statements is True or False.

a) Normal distribution curve with mean 16 and standard deviation 5 is wider than normal curve with mean 16 and standard deviation 3.

True False

b) If we compute 95 % and 90% confidence intervals for the mean final exam score of all Mat 117 students at ASU last semester then 90% confidence interval will be wider than 95% confidence interval.

True False

c)For [pic], [pic] for the t distribution curve with 7 degrees of freedom will be a smaller number than [pic]

True False

d) Margin of error in 90% confidence interval for [pic]decreases with increasing sample size.

True False

e) 80th percentile of N(0,1) =[pic]

True False

f) Consider the normal curve with mean 10 and standard deviation 4 . According to Empirical Rule 68.26% of the area under that curve is between 6 and 14.

True False

g)If normally distributed variable X has mean [pic]=16 and standard deviation [pic]=5 then [pic]has standard normal distribution.

True False

h) Suppose the mean annual income for adult women in one city is $28,520 with standard deviation of $5190 and the distribution is extremely left skewed. For the samples of size 99, [pic]has approximately normal distribution.

True False

Question #1 continues on the next page.

i) Suppose 90% confidence interval for a mean age of participants in a large mathematical conference , based on a random sample of 120 participants, is (35, 49). We can say that 90% of people in the sample are between 35 and 49 years old.

True False

j) If events A,B are mutually exclusive with P(A)=0.2 and P(B)=0.5, then P(A or B)=0.7

True False

k) Using a simple random sample of size 5 we can compute a confidence interval for mean age of some large population using z-interval procedure if we know population standard deviation, but population is not normally distributed.

True False

l) If eight decile of N(0,1) =A then second decile of N(0,1) = -A

True False

m) If [pic] is the sample mean for the sample of size n=16 from normal population with mean 20 and standard deviation 8, then variable [pic]has N(0,1) distribution

True False

n) Sampling error in estimating population mean by the sample mean increases with increasing sample size.

True False

o) For normally distributed variable X with mean 10 and standard deviation 4 ,

P(X>16) =P(Z>1.5) , where Z has N(0,1) distribution.

True False

p) Suppose sample of size=62 from some large population has [pic]=12 and s=12, we can use t-interval procedure for the confidence interval for the population mean even if population has left skewed distribution.

True False

q) Suppose probability of you passing this test is 0.75, then probability of you failing it is 25%.

True False

Question #2 Medical Tests on Emergency Patients.

The frequency distribution shown below illustrates the number of medical tests conducted on 36 randomly selected emergency patients.

|Number of Tests |0 1 2 3 4 or more |

|Number of patients |12 8 5 5 6 |

Suppose one patient is selected at random, compute following probabilities, leave answers in fraction form

(a)(4 points) Probability that this patient had exactly 2 tests done

ANSWER:___________________

(b) (4 pts) Probability that this patient had at least 1 tests and no more than 2 tests

done.

ANSWER:___________________

Question #3. College Degrees Awarded.

The relative frequency table below represents college degrees awarded in recent academic year by gender (at ASU)

| |Bachelor's |Master's |Doctorate |

|Male |0.310 |0.101 |0.013 |

|Female |0.407 |0.158 |0.011 |

Suppose a degree is randomly selected. Compute the following probabilities:

a) (4 points) Probability that the degree is not a master's degree.

ANSWER:___________________

b)(4 points) Probability that that degree is awarded to a man or it is a master's

degree

ANSWER:___________________

Question #4. Standard Normal Curve.

Use the tables of standard normal curve or a calculator to find the following. Include appropriate sketch explaining each answer.

a. (4 points) area between - 1.32 and 1.19

ANSWER:___________________

b. (4 points) area left of -2.15

ANSWER:___________________

c. (4 points) 58th percentile of the standard normal curve

ANSWER:___________________

Question #5. Chocolate Bar Calories.

The number of calories in a certain 1.5-ounce chocolate bar has normal distribution with mean 225 with standard deviation of 10 calories.

Answer following questions, include appropriate sketch explaining your answer.

a) ( 4 points) What percentage of chocolate bars will have number calories exceeding 255 calories?

ANSWER:___________________

b)(4 points) How many calories are in a chocolate bar that is in 95th percentile of that distribution?

ANSWER:____________________

Question #6 SAT Scores.

The national SAT test scores (for Verbal and Math)) have normal distribution with a

mean [pic] =1025 points and standard deviation [pic]= 90 points

a) (4 points)Let [pic] be a sample mean for the samples of size 9 from all the SAT

scores. What is the sampling distribution of [pic]? Give mean and standard

deviation of that distribution.

Sampling distribution of [pic]is __________________________________

[pic]= _______________ [pic]=_________________________

b)(4 points) Suppose we select a random sample of 9 SAT scares and [pic] is their average. What is the probability that [pic] be smaller than 940?

P([pic]< 940)=__________________________________

Question #7 Body Temperature

A study reports that oral body temperature for a random sample of 30 healthy adults living in AZ had a sample mean of 98.25 degrees Fahrenheit. Suppose we know that population standard deviation is 0.73 degrees Fahrenheit.

a) (8 points)Find 80% Confidence Interval (CI) for [pic]=mean number of nights all AZ residents stayed in a hotel during their vacations last year. Use z-interval procedure.

Give margin of error in your CI: ____________________

Compute both endpoints of your CI: _____________________

d) ( 4 points) What sample size is needed so that margin of error in our 80% CI will be 0.05?

n=_________________________________________

Question #8 Length of Children's Animated Films.

A data below represents lengths (in minutes) for a random sample of 12 popular children's animated films. Let [pic] be the true average length of all children's animated films. Assume normal distribution.

74, 76, 77, 78, 78, 76, 81, 83, 81, 83, 85, 92

a) (4 points) Compute a point estimate of [pic]

ANSWER:_________________________________

b)(4 points) Suppose you wanted to compute 90% confidence interval for [pic] and use a t-interval procedure. What is the appropriate t-value you need to use in computing of a margin of error in your confidence interval, make sure to use appropriate degrees of freedom.

Select correct answer:

A) t=1.363 B) t=1.796 C) t=1.372 D) t=1.812

ANSWER:_________________________________

c)(4 points) Suppose 95 % confidence interval for [pic] is: (77.2 min , 83.5 min ).

Based on that interval do you think it is reasonable to assume that [pic] is more than 1.25 hours (75 min)? Select appropriate answer from the following:

i) Yes, because both endpoints of the CI are above 75min.

ii) No, because 75 min is outside of the CI .

iii) Yes, because sample mean is more than 75 min

iv) No, because lower endpoint of CI is only few minutes above 75min

ANSWER:_________________________________

d) (4 points) Without computations will 99% CI for [pic] be wider then, narrower than or the same as 90% CI for [pic]? Select appropriate answer:

A) wider B) narrower C) the same

[pic]

[pic]

[pic]

[pic]

FORMULAS

Sample statistics

Sample mean: [pic], Sample standard deviation (definition) [pic]

Computational formula [pic]

Population parameters:

Population mean: [pic] Population standard deviation: [pic] or [pic]

Standard score or z-score [pic] If [pic]then [pic]

Probability

P(E)=f/N P(A or B) = P(A) + P(B) - P(A and B)

Sampling Distribution of [pic]

[pic] , [pic], Standardized version of [pic]: [pic]

Confidence Intervals for [pic]

Confidence level C=[pic]

Z-interval: [pic] Margin of error: [pic], Sample size estimation: [pic]

t-interval: [pic], df=n-1, Studentized version of [pic]: [pic]

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