General Questions
What chapters are on the exam?
Chapter 6,7,9&10
When she is asking for the mean in random variable and binomial problems, she is asking for the ______ (not average)
expected value
We can use normal distribution for a binomial when:
n is large
Name one of the assumptions and conditions for sample proportions.
1) values must be independent
2) np>= 10, nq >=10
3) sample size no larger than 10% of population
4) randomized
The opposite of the null hypothesis is the:
alternative hypothesis
If we aren't given p and q, we use:
.5 for both
For random variable problems, what do the probabilities add up to?
1
The percents for the empirical rule are:
those can each be broken into halves of:
68%-95%-99.7%
34%-47.5%-49.85%
What is the mean of a sample proportion?
p, the true proportion
Write the symbols for
1)one-tailed tests
2) two-sided
1) p> Po, p< Po
2) p ≠ Po
What is the range a p-value can be?
0< p-value <1 (between 0 and 1)
The probability of having no kids is .23, of one kid is .2, of two kids is .43, and three kids is .14
1) find the mean and standard deviation
1) use 1-var stats: mean= 1.48, SD= .9948
A student got her scores back. She got a 580 and was at the lower 16th percentile. The report said the SD of scores was 48. What is the mean of the scores?
68% in the middle leaves 16% on each tail. Add the SD to her score: 580+48=628 as the mean
Describe the sampling distribution of the following: A study found that the retention rate was 74%. In a random sample of 103, 81% returned.
p^~ AN(.74, .0432)
When a significance level is not given use:
Alpha= .05
What calculator function do we use for a binomial with a sample size of 200 and a p=.4? Explain
Use Normalcdf because n is large. np and nq are both greater than 10 so we can assume the binomial is approximately normal.
It is known that 20% of college students work full time. If we randomly select 12 students, what is the probability that at least 3 of the 12 work full time?
n=12, p=.2
1- binomcdf (12,.2,2)= .4417
The distribution of heights for college women is normal, mean= 65 inches, SD= 2.7 inches.
Find the height such that 10% of college women are shorter than that height.
first find z-score= -1.28
then use inverse formula x=z(SD) + mean
x= (-1.28)(2.7)+65= 61.544 inches
Suppose 13% of pop. is left handed. A classroom has 15 lefty-desks. The class has a random sample of 90 students. What is the probability that more than 17% of the sample of 90 is left handed? (so there is not enough desks for left-handed people)
1-.8708=.1292
Complete the 5 steps for hypothesis testing for the following:In 2004, 5.8% of job applicants who were tested for drugs failed the test. Test the claim that the failure rate is now lower if a random sample of 1520 current applicants results in 58 failures.
1) Ho: Po= .058, Ha: Pa< .058
2) z= -3.3
3) p-value= .0005
4) P-value< alpha, reject Ho
5) Evidence indicates that the drug test failure rate is less than 5.8%
30% wear contact lenses. A random sample of 100 students is selected.
1) describe the sample of 100 students selected.
2) what is the probability that more than 1/3rd of this sample wear contacts?
1) p^~AN(.3,.0458)
2)1-.7673=.2327
25% of the customer entering a grocery store between 5-7pm use an express checkout. We select 5 customers at random.
1) describe the distribution
2)What is the probability that exactly 3 of the 5 use express checkout?
3)What is the probability that at least 2 use express?
4) calculate the mean and SD
1) x~B(5,.25)
2)BinomPdf (5,.25,3)= .0879
3) 1- binomcdf (5,.25, 1)= .6328
4) np= 1.25, SD= sq rt of npq= .9682
People with a gene have 0.7 probability of getting a certain disease. 100 participate in a study.
1) Write the notation
2)Suppose you found 78 contracted the disease. Is this too high? Justify by finding probability at least 78 contract the disease.
2) P(x>78), use normalcdf (78,1000000, 70, 4.5826) which equals .0404, this is a small value and compared to an alpha of .05 (use if no alpha given), it is very unlikely to have at least 78 contract the disease
Find the point estimate and margin of error for the following:
A random sample of 200, confidence interval of 90% and the confidence interval is (0.0520, 0.1188).
p^= LB+UB/2= .0854
ME= UB-LB/2= +-.0334
We calculate a 90% CI for p is (.53,.67) and want ti test the following: Ho= .5, Ha≠.5
1)What would the statistical decision be? Why?
2) What would the level of significance be?
3) If your decision had been a mistake, what type of error would you have made?
1) Reject Ho because .5 is not in the interval
2) 90%, alpha= 1-.9=.1
3) Type I