The manufacturer claims that your new car gets 31 mpg on the highway. You suspect that the mpg is a different number for your car. The 40 trips on the highway that you took averaged 28.7 mpg and the standard deviation for these 40 trips was 5.8 mpg. What can be concluded at the α α = 0.01 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? μ p ? ≠ = > < H1: H1: ? μ p ? > < = ≠ c.The test statistic ? t z = (please show your answer to 3 decimal places.) d.The p-value = (Please show your answer to 4 decimal places.) e.The p-value is ? ≤ > α α f.Based on this, we should Select an answer reject fail to reject accept the null hypothesis. g.Thus, the final conclusion is that ... The data suggest that the sample mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 28.7. The data suggest that the population mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 31. The data suggest that the populaton mean is significantly different from 31 at α α = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 31. h.Interpret the p-value in the context of the study. There is a 1.64116434% chance of a Type I error. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway then there would be a 1.64116434% chance that the population mean would either be less than 28.7 or greater than 33.3. There is a 1.64116434% chance that the population mean mpg for your car on the highway is not equal to 31. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway, then there would be a 1.64116434% chance that the sample mean for these 40 highway trips would either be less than 28.7 or greater than 33.3. i.Interpret the level of significance in the context of the study. There is a 1% chance that you own an electric powered car, so none of this matters to you anyway. If the population population mean mpg for your car on the highway is different from 31 and if you take another 40 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 31. There is a 1% chance that the population mean mpg for your car on the highway is different from 31. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is different from 31.

1) The red blood cells counts of women are normally distributed with a mean of 4.577 and a standard deviation of 0.382.

Find the probability that a randomly selected woman has a red blood cell count that is lower than 4.2.

(Results are rounded to 4 decimal places)

a) 0.1618

b)  0.8382

c)  0.3382

d) 0.7979

2) A KRC research poll asked respondents if they felt vulnerable to identity theft. Of 1002 people polled, 531 said "yes".

Find a 95% confidence interval for the proportion of people who felt vulnerable to identity theft.

(Results are rounded to 4 decimal places)

a)  (0.5034, 0.5564)

b)  (0.4990, 0.5608)

c)   (0.4769, 0.5829)

d)   (0.5041, 0.5559)

Use repetitions to solve it. Don't simplify answer

(1) 20 different comic books will be distributed to five kids. How many ways are there to distribute the comic books if they are divided evenly so that 4 go to each kid?

(2) A family has four daughters. Their home has three bedrooms for the girls. Two of the bedrooms are only big enough for one girl. The other bedroom will have two girls. How many ways are there to assign the girls to bedrooms?

(3) A camp offers 4 different activities for an elective: archery, hiking, crafts and swimming. The capacity in each activity is limited so that at most 35 kids can do archery, 20 can do hiking, 25 can do crafts and 20 can do swimming. There are 100 kids in the camp. How many ways are there to assign the kids to the activities?

(4) A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals. How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?

Houseflies have short lifespans. Males of a certain species have lifespans that are strongly skewed to the right with a mean of 26 days and a standard deviation of 12 days. a) Explain why you cannot determine the probability that a given male housefly will live less than 24 days. b) Can you estimate the probability that the mean lifespan for a sample of 5 male houseflies is less than 24 days? Explain. c) A biologist collects a random sample of 65 of these male houseflies and observes them to calculate the sample mean lifespan. Describe the sampling distribution of the mean lifespan for samples of size 65. d) What is the probability that the mean lifespan for the sample of 65 houseflies is less than 24 days? e) What is the mean lifespan for the top 15% of samples of size 65?

A.

Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.

B. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

B-2. Find the p-value.

B-3. Do you reject the null hypothesis at the 1% level?

C. Do you reject the null hypothesis at the 10% level?

The average salary for American college graduates is $42,900. You suspect that the average is less for graduates from your college. The 49 randomly selected graduates from your college had an average salary of $38,173 and a standard deviation of $10,190. What can be concluded at the αα = 0.01 level of significance?

1. For this study, we should use Select an answert-test for a population meanz-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:   ?pμ ?=≠><   

H1:H1:   ?pμ ?><≠=

3. The test statistic ?tz = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?>≤ αα
6. Based on this, we should Select an answeracceptfail to rejectreject the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly less than 42,900 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is less than 42,900.
   • The data suggest that the population mean is not significantly less than 42,900 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is less than 42,900.
   • The data suggest that the sample mean is not significantly less than 42,900 at αα = 0.01, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is less than 38,173.
8. Interpret the p-value in the context of the study.
   • If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 0.10651237% chance that the population mean salary for graduates from your college would be less than $42,900.
   • There is a 0.10651237% chance that the population mean salary for graduates from your college is less than $42,900.
   • If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 0.10651237% chance that the sample mean for these 49 graduates from your college would be less than $38,173.
   • There is a 0.10651237% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • There is a 1% chance that your won't graduate, so what's the point?
   • There is a 1% chance that the population mean salary for graduates from your college is less than $42,900.
   • If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for graduates from your college is less than $42,900.
   • If the population population mean salary for graduates from your college is less than $42,900 and if another 49 graduates from your college are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $42,900.

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.19 days. Is this average shorter for blind dates? A researcher interviewed 58 couples who had recently been on blind dates and found that they averaged 3 days to communicate with each other after the date was over. Their standard deviation was 0.639 days. What can be concluded at the  αα = 0.01 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:   ?μp ?><≠=   

H1:H1:   ?pμ ?≠=<>

3. The test statistic ? tz = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?>≤ αα
6. Based on this, we should Select an answerfail to reject accept reject the null hypothesis.
7. Thus, the final conclusion is that
   • The data suggest that the population mean is not significantly less than 3.19 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.19.
   • The data suggest the populaton mean is significantly less than 3.19 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.19.
   • The data suggest the population mean is not significantly less than 3.19 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is equal to 3.19.

Of the following, which is a reason we take samples instead of taking a census?

A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow.

The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.

Develop the null and alternative hypotheses.
H 0 =  d Selectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10Item 1  
H a =  d Selectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10Item 2  

Calculate the value of the test statistic. If required enter negative values as negative numbers. (to 2 decimals).
  

The p-value is Selectless than .01between .10 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 4  

Can you conclude that the price differential is not equal to $10?
SelectYesNoItem 5  

What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)? Use z-table.
( ,  )

3.3) A small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with the following pmf.

Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.]

*What is the expected profit if three magazines are ordered? (Round your answer to two decimal places.)

*What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.)

*How many magazines should the store owner order?

-3 magazines

-4 magazines

Based on historical data, your manager believes that 33% of the company's orders come from first-time customers. A random sample of 102 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.27? Note: You should carefully round any z-values you calculate to 4 decimal places.

Answer =

(Enter your answer as a number accurate to 4 decimal places.)

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 65 and estimated standard deviation σ = 31. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

The probability distribution of x is not normal.The probability distribution of x is approximately normal with μ_x = 65 and σ_x = 21.92.    The probability distribution of x is approximately normal with μ_x = 65 and σ_x = 31.The probability distribution of x is approximately normal with μ_x = 65 and σ_x = 15.50.

What is the probability that x < 40? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)


(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

YesNo    

Explain what this might imply if you were a doctor or a nurse.

The more tests a patient completes, the weaker is the evidence for excess insulin.The more tests a patient completes, the stronger is the evidence for excess insulin.    The more tests a patient completes, the weaker is the evidence for lack of insulin.The more tests a patient completes, the stronger is the evidence for lack of insulin.

Suppose that finishing times of runners in a local 10K race follow an approximate normal distribution with mean 61 minutes and standard deviation 9 minutes.

(a) Melissa finished the race in 52 minutes. How many standard deviations below average is Melissa's time?

(b) What is the probability that a randomly selected runner completed the race in between 43 and 52 minutes?

(c) Jennifer's finishing time was 79 minutes. What percentage of runners had faster times than Jennifer?

(d) The fastest 16% of runners finished the race in less than how many minutes?

If n = 240 and ˆ p (p-hat) = 0.7, construct a 99% confidence interval. Give your answers to three decimals

< p <