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Scott
Scott, MIT Graduate
Category: Math Homework
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hey scott i have a math test due and i have few questions could

Resolved Question:

hey scott i have a math test due and i have few questions could you answer them?
Submitted: 5 years ago.
Category: Math Homework
Expert:  Scott replied 5 years ago.

Hi there,

 

What type of questions? Please post them and I'll let you know if I can help.

 

-Scott

Customer: replied 5 years ago.
there math questions for statistics
Expert:  Scott replied 5 years ago.

Is it timed? If it's not timed, plese post them.

-Scott

Customer: replied 5 years ago.
it is timed for 3hours and i have like 5 written responses i beleive but i havent started the test i just wanted to know i have someone to answer the written while iw ork on the multiple you have actually helped me before but this one is for a friend that wanted someone smart and i thought u were the best one whose helped me in math.
Expert:  Scott replied 5 years ago.

Ok, if it's timed, I'd want to see some sample problems before I can commit, please. I don't want to start the timer and then not be able to help.

Thanks,

-Scott

Customer: replied 5 years ago.
there like average, mode, median, leaf charts, biniomial deviations, etc statistic problems, probability

questions like this u answered last year for me



1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.
Company X claims that the average salary for an entry level employee is $35,000 (Points : 8)


2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18 minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)
Expert:  Scott replied 5 years ago.

Ok, that's fine! Go ahead with the real ones.

-Scott

Customer: replied 5 years ago.
okay thanks

For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.
An automobile tire manufactory claims than their tires last more than 70,000 miles before needing replacement. (Points : 8)

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager’s claim at alpha =.05? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)


3. (TCO 5) At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not.
(a) Is this a binomial experiment? Explain how you know.
(b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. Show your calculations or explain how you found the probability.
(Points : 20)


4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.
(a) Find the probability of having a utility bill between 135 and 170.
(b) Find the probability of having a utility bill less than $135.
(c) Find the probability of having a utility bill more than $180. (Points : 20)


5. (TCO 8) A Mall manager claims that in average every customer spends $52 per a single visit to the mall. To test this claim, you took a sample of 36 customers and found the sample mean to be $55 and the sample standard deviation to be $12. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)


6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 55 businesses, he found that mean number of transaction per month to be 32 and the standard deviation to be 7.5 transactions.
(a) Find a 90% confidence interval for the mean number of business transactions per month. 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. (Points : 20)


7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 500 products, he found 30 defective products.


(a) Find a 98% confidence interval for the true proportion of defective product. 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.
(Points : 20)


8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}


(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? (Points : 20)
Expert:  Scott replied 5 years ago.

Ok, I'll get started.

-Scott

Customer: replied 5 years ago.
thanks
Expert:  Scott replied 5 years ago.

No problem!

-Scott

Expert:  Scott replied 5 years ago.

Here you go:


For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.
An automobile tire manufactory claims than their tires last more than 70,000 miles before needing replacement. (Points : 8)
H0: μ <= 70000
Ha: μ > 70000

 

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager's claim at alpha =.05? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

H0: μ <= 25
Ha: μ > 25

 

The critical z value is: 1.6449

 

Test statistic:

z = (x-mu)/(s/sqrt(N))

= (26.5-25)/(4/sqrt(49))

= 2.625

 

That's greater than the critical value.

We reject H0, and conclude that the mean is greater than 25 minutes.

 

3. (TCO 5) At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not.
(a) Is this a binomial experiment? Explain how you know.


Yes, it's a binomial experiment, because the probability is constant, events are independent, and there is a fixed number of trials.

 


(b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. Show your calculations or explain how you found the probability.
(Points : 20)

Using the binomial formula:

N choose X * p^X * p^(N-X)

25 choose 10 * 0.35^10 * 0.65^15

=(NNN) NNN-NNNN* 0.35^10 * 0.65^15

= 0.14085

 

 

4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.
(a) Find the probability of having a utility bill between 135 and 170.
z(135) = (135-150)/20 = -0.75
z(170) = (170-150)/20 = 1
prob(-0.75 < z < 1) from a table:
0.6147


(b) Find the probability of having a utility bill less than $135.
prob(z < -0.75)
0.2266


(c) Find the probability of having a utility bill more than $180. (Points : 20)
z(180) = (180-150)/20 = 1.5
prob(z > 1.5)
0.0668

 

 

5. (TCO 8) A Mall manager claims that in average every customer spends $52 per a single visit to the mall. To test this claim, you took a sample of 36 customers and found the sample mean to be $55 and the sample standard deviation to be $12. At alpha = 0.05, test the Mall's manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

H0: μ = 52
Ha: μ ≠ 52

 

The critical values are +/- 1.96.

The z value is:

z = (x-mu)/(s/sqrt(N))

z = (55-52)/(12/sqrt(36))

z = 1.5

 

That's not outside the critical values.

We do not reject H0, and conclude the mean is not different from $55.

 

 

6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 55 businesses, he found that mean number of transaction per month to be 32 and the standard deviation to be 7.5 transactions.
(a) Find a 90% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval.

z(90%) = 1.6449
mean - z*sd/sqrt(N) to mean + z*sd/sqrt(N)
32 - 1.6449*7.5/sqrt(55) to 32 + 1.6449*7.5/sqrt(55)
30.3365 to 33.6635


(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)
This means that we are 90% confident that the true mean number of transactions is between these two values.

 

 

7. (TCO 7) A company's CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 500 products, he found 30 defective products.

(a) Find a 98% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.

p = 30/500 = 0.06

The interval goes from:

p-z*sqrt(p*(1-p)/N) to p+z*sqrt(p*(1-p)/N)

0.06-2.326*sqrt(0.06*0.94/500) to 0.06+2.326*sqrt(0.06*0.94/500)

0.035296 to 0.084704

 


(b) Interpret this confidence interval and write a sentence that explains it.

This means we are 98% confident that the true population proportion lies between these values.

 

 

8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}


(a) Find the mean, median, mode, sample variance, and range.
mean
=AVERAGE(17,20,18,24,21,26,29,18,22,28)
= 22.3
median
=MEDIAN(17,20,18,24,21,26,29,18,22,28)
= 21.5
mode
=MODE(17,20,18,24,21,26,29,18,22,28)
= 18
var
=VAR(17,20,18,24,21,26,29,18,22,28)
= 18.4556
range
= max - min
= 12


(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)
Since the mean, median, and mode aren't very close, I don't think these are from a normal.

 

Let me know if you have any questions, and if you're set, thanks for accepting!
Scott

Customer: replied 5 years ago.
thanks scott i hav a couple multiple choice im stuck on is it okay if you help me on them
Expert:  Scott replied 5 years ago.

You can post them, and I'll see if I can help.

-Scott

Customer: replied 5 years ago.
okay thanks


At a drive through window of a bank it’s found that 10 customers get served every 15 minutes. The bank’s manage is interested in finding a way to increase the number of customers that can be served. He thought that knowing the probability of serving 12 customers per 15 minutes could be helpful to him in the decision making process. Choose the best answer of the following: (Points : 6) 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
Expert:  Scott replied 5 years ago.

Ok:

This is an example of a Poisson probability experiment

 

Thanks for accepting for all the written ones and this one!

-Scott

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