Question

HW9-Practice: Problem 3

**Problem Value**: 1 point(s). **Problem
Score**: 50%. **Attempts Remaining:**
Unlimited.

(1 point) Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the standard deviation is 5.2 MPG. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed. Report all answers to 4 decimal places.

**1.** We would like to use these data to evaluate
the average gas mileage of all 2012 Prius drivers. Do you think
this is reasonable? Why or why not?

? Yes No , because ? the data distribution seems approximately normal there are 14 data points in the sample user estimates are reliable user estimates are not reliable .

The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? Conduct a hypothesis test. Round numeric answers to 3 decimal places where necessary.

**2.** What are the correct hypotheses for
conducting a hypothesis test to determine if these data provide
strong evidence against this estimate for drivers who participate
on fueleconomy.gov? (Reminder: check conditions)

**A.** ?0:?=50H0:μ=50 vs. ??:?≠50HA:μ≠50

**B.** ?0:?=53.3H0:μ=53.3 vs. ??:?≠53.3HA:μ≠53.3

**C.** ?0:?=50.3H0:μ=50.3 vs.
??:?<50HA:μ<50

**D.** ?0:?=50H0:μ=50 vs. ??:?>50.3HA:μ>50.3

**3.** Calculate the test statistic.

**4.** Calculate the p-value.

**5.** How much evidence do we have that the null
model is not compatible with our observed results?

**A.** extremely strong evidence

**B.** little evidence

**C.** very strong evidence

**D.** strong evidence

**E.** some evidence

**6.** Calculate a 95% confidence interval for the
average gas mileage of a 2012 Prius by drivers who participate on
fueleconomy.gov.

( , )

Answer #1

1)Yes because the data distribution seems approximately normal

2)

option A

3)

population mean μ= | 50 |

sample mean 'x̄= | 53.300 |

sample size n= | 14.00 |

sample std deviation s= | 5.200 |

std error 'sx=s/√n= | 1.390 |

test stat t ='(x-μ)*√n/sx= |
2.3745 |

4)

p value = | 0.0337 |

5)

**C.** very strong evidence

6)

for 95% CI; and 13 df, value of t= | 2.1604 | |

margin of error E=t*std error = | 3.0024 | |

lower bound=sample mean-E = | 50.2976 | |

Upper bound=sample mean+E = | 56.3024 | |

from above
95% confidence interval for population mean =(50.2976
,56.3024) |

HW8-Practice: Problem 4
Problem Value: 1 point(s). Problem
Score: 29%. Attempts Remaining:
Unlimited.
(1 point) In the recent report, "State of the American
Workplace," Gallup.com stated that 30% of the U.S workforce is
"engaged" in their work, 52% are "not engaged," and 18% are
"actively disengaged." Using their survey methods, the manager of a
large department store collects similar data on a random sample of
the store's employees. Round all numeric answers to 4 decimal
places.
Engagement
Frequency
Engaged
96...

****PLEASE ANSWER ALL QUESTIONS****
Question 12 (1 point)
A medical researcher wants to determine if the average hospital
stay of patients that undergo a certain procedure is greater than
8.7 days. The hypotheses for this scenario are as follows: Null
Hypothesis: μ ≤ 8.7, Alternative Hypothesis: μ > 8.7. If the
researcher takes a random sample of patients and calculates a
p-value of 0.0942 based on the data, what is the appropriate
conclusion? Conclude at the 5% level of significance....

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