Download 1. For the following statement, write the null hypothesis and the

1. For the following statement, write the null hypothesis and the alternative hypothesis. Then,
label the one that is the claim being made. The mean life of a car?s engine is no more than 10
years.
Ho: u ≤ 10 claim
Ha: u >10
2.A 15-minute Oil and Lube service claims that their average service time is no more than 15
minutes. A random sample of 40 service times was collected, and the sample mean was found to
be 15.4 minutes, with a sample standard deviation of 3.2 minutes. Is there evidence to support, or
to reject the claim at the alpha = 0.02 level? Perform an appropriate hypothesis test, showing the
necessary calculations and/or explaining the process used to obtain the results.
Ho: u ≤ 15
Ha: u >15
t-statistic = (15.4-15)/(3.2/40)=0.791
Critical value = t(39,0.02)=2.125
We don´t reject Ho since the statistic is less than 2.125, there is no enough evidence to
reject the claim
3.The probability that a house in an urban area will be burglarized is 5%. If 50 houses are
randomly selected, what is the probability that one of the houses will be burglarized?
(a) Is this a binomial experiment? Explain how you know.
(b) Use the correct formula to find the probability that, out of 50 houses, exactly 4 of the houses
will be burglarized. Show your calculations or explain how you found the probability.
a) Yes, experiments are independent and each of them has only 2 results (burglarized or
not) ( X=number of houses burglarized in the sample )
b) X has a binomial distribution n=50, p =0.05, X = number of houses burglarized
P(X=4)= (50C4)(0.05)4(0.95)46=0.136
4.The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a
normal distribution with a standard deviation of 10 gallons. A family is chosen at random.
(a) Find the probability that the family’s monthly gasoline purchases will be between 86 and 96
gallons.
(b) Find the probability that the family’s monthly gasoline purchases will be less than 87 gallons.
(c) Find the probability that the family’s monthly gasoline purchases will be more than 75 gallons.
X has a normal distribution with mean =90, sd = 10
Z = (X-90)/10 has a standard normal distribution
a) P(86<X<96)=P(-0.4<Z<0.6)=0.3812
b) P(X<87)=P(Z<-0.3)=0.3821
P(X>75)=P(Z>-1.5)=0.9332
5.An engineering firm is evaluating their back charges. They originally believed their average back
charge was $1800. They are concerned that the true average is higher, which could hurt their
quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample
mean back charge to be $1950. If the standard deviation of back charges is $500, and alpha = 0.01,
should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the
necessary calculations and/or explaining the process used to obtain the results.
Ho: u ≤ 1800
Ha: u >1800
z-statistic = (1950-1800)/(500/40)=1.897
Critical value = z(0.05)=1.645
We reject Ho since the statistic is greater than 1.645, there is enough evidence to be
concerned
6. A marketing firm wants to estimate the average amount spent by patients at the hospital
pharmacy. For a sample of 200 randomly selected patients, the mean amount spent was $92.75
and the standard deviation $13.10.
(a) Find a 95% confidence interval for the mean amount spent by patients at the pharmacy. Show
your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it.
a) CI at 95% for the mean is 92.75±t(199,0.025)13.1/200 = (90.923, 94.577)
b) We are 95% confident that the mean is in the interval, we can´t say that the probability
that the mean is in the interval is 95%, The probability that the confidence interval
(random) contains the mean is 95%
7.A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart
condition. Because the condition is rare, the manufacturer can only find 18 people with the
condition currently untreated. From this small sample, the mean heart rate is 93 beats per minute
with a standard deviation of 6. (a) Find a 98% confidence interval for the true mean heart rate of
all people with this untreated condition. Show your calculations and/or explain the process used
to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.
8.The heights of 10 sixth graders are listed in inches: {50, 62, 54, 57, 60, 57, 53, 57, 59, 58}.
(a) Find the mean, median, mode, sample variance, and range.
(b) Do you think that this sample might have come from a normal population? Why or why not?
a) mean =56.7, median =57, mode =57, sample variance =3.529, range = 12
b) yes because mean and the median are close
1. The annual Salary of an electrical engineer is given in terms of the years of experience by
the table below. Find the equation of linear regression for the above data and obtain the
expected salary for an engineer with 45 years of experience.
Round to the nearest $100. 87,600 88,100 55,400 90,500
I need the table to do this question
2. A company produces window frames. Based on a statistical analysis, we found that 15% of
their product is defective. They have shipped 10 windows to one of their customers. The
customer is worried about the probability of having defective frames. Choose the best
answer of the following:
This is an example of a Poisson probability experiment
This is an example of a Binomial probability experiment
This is neither a Poisson nor a Binomial probability experiment
Not enough information to determine the type of experiment
3. A test is composed of six multiple choice questions where each question has 4 choices.
If the answer choices for each question are equally likely, find the probability of answering
3 OR 4 questions correctly. 0.131836 0.032959 0.004639 0.164795
3. It has been recorded that the average number of errors in a newspaper is 4 mistakes per
page. What is the probability of having 1 or 2 errors per page?
Answer: 0.3419