Statistical Methods I (MAT 152) Questions

A population of values has a normal distribution with u=163.1 and o=67.1 . You intend to draw a random sample of size n=176 . Find the probability that a single randomly selected value is between 174.7 and 176.3. P(174.7 < X < 176.3) = Find the probability that a sample of size n=176 is randomly selected with a mean between 174.7 and 176.3. P(174.7 < M < 176.3) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.187.

Consider your next 49 purchases that produce a game piece. Calculate the following:

For parts (a) through (c), express your answer as a decimal with 4 decimal places.

a) What is the probability that you win 10 prizes? 

b) What is the probability that you win more than 11 prizes?  

c) What is the probability that you win between 8 and 11 (inclusive) prizes?  

d) What is the probability that you win 6 prizes or fewer?  

Assume that a procedure yields a binomial distribution with a trial repeated n=5 times. Use some form of technology to find the probability distribution given the probability p=0.718 of success on a single trial.

(Report answers accurate to 4 decimal places.)

k

P(X = k)

Assume that a procedure yields a binomial distribution with a trial repeated n=11 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=2 successes given the probability q=0.28 of failure on a single trial.

(Report answer accurate to 4 decimal places.)

P(X=k)=

Assume that a procedure yields a binomial distribution with a trial repeated n=20 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=5 successes given the probability p=3/10 of success on a single trial.

(Report answer accurate to 4 decimal places.)

P(X=k)= 

Assume that a procedure yields a binomial distribution with a trial repeated n=13 times. Use either the binomial probability formula (or technology) to find the probability of k=5 successes given the probability p=60% of success on a single trial.
 

P(X=k)= 

(Report answer accurate to 4 decimal places.)



 

Testing:

H0: p =0.36
H1: p ≠0.36

Your sample consists of 149 subjects, with 49 successes. Calculate the test statistic, rounded to 2 decimal places

z=

A population of values has a normal distribution with u=137.2 and o=41.1. You intend to draw a random sample of size n=23.

Find the probability that a sample of size n=23 is randomly selected with a mean between 126.1 and 163.8.
P(126.1 < M < 163.8) = 

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

 

Assume that a sample is used to estimate a population mean u. Find the margin of error M.E. that corresponds to a sample of size 23 with a mean of 36.3 and a standard deviation of 6.9 at a confidence level of 99.5%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. = 

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $49 and standard deviation of $15. Construct a confidence interval in the form estimate±margin of error at a 98% confidence level.

In a survey, 16 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $50 and standard deviation of $6. Estimate how much a typical parent would spend on their child's birthday gift (use a 90% confidence level).

Give your answers to one decimal place. Provide the point estimate and margin or error.
 

 If n=14, x¯=31, and s=9, construct a confidence interval at a 95% confidence level. Give your answers to one decimal place.

You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
56.3
64.1
69.8
75.1
69.7
45.6
65
57.6

Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).

98% C.I. =

Answer should be obtained without any preliminary rounding.
 

H0: p =0.62
H1: p >0.62

Your sample consists of 93 subjects, with 55 successes. Calculate the test statistic, rounded to 2 decimal places

z=