Project #28219 - statiscis

 

1. Nation-wide, the percentage of households with more than one television is 73%. John 

thinks the percentage in his neighborhood is lower. He makes a random survey of the 

houses in his neighborhood and finds that, of the 127 households surveyed, 85 have more 

than one television. Does his data support his claim? Make sure you do the test to see if the 

sample is large enough to use the normal approximation. 

A) (2 point) State the claim and the alternate hypothesis (H1) ( ≠p0; <p0; >p0 ) 

 

 

B) (2 point) What type of test used to evaluate the owner’s claim? 

 

C) (4 points) With an  = 0.10, is the proportion lower in John’s neighborhood? 

 What is the p-value? 

 

 

 Do you Reject the Null Hypothesis or Not Reject the Null Hypothesis? 

 State the result (whether the data supports the claim or not). 

 

 

 

 

 

2. The speed limit on a certain section of I-70 is 65 mph. I think the average speed of cars on 

this section is over the speed limit. Using a speed radar system, I find that the average speed 

of a random sample of 30 cars on this section of I-70 is 66.9. The population standard 

deviation for the speeds is known to be 6.8 mph. At a significance level of 0.05, is the 

average speed on this section of I-70 above the speed limit? Assume the speeds are 

normally distributed. 

A) (2 points) State the claim and the alternate hypothesis (H1) ( ≠μ0; <μ0; >μ0 ) 

 

 

B) (2 point) What type of test used to evaluate the claim (z-Test or t-Test)? 

 

C) (4 points) With an  = 0.05, is the average speed above the speed limit? 

 What is the p-value? 

 

 

 Do you Reject the Null Hypothesis or Not Reject the Null Hypothesis? 

 State the result (whether the data supports the claim or not). 

 

 

 

 

 

For all questions, in addition to your answer, please 

write down what you entered into your calculator. Homework Assignment #8 – Intro to Statistics – MTH115 – Spring 2014

Page 2 

3. To improve fuel efficiency, the owner of a trucking company installs a new type of catalytic 

converter in his trucks. He claims the converter will increase fuel mileage. Before 

installation, his trucks had a mean fuel mileage of 7.0 mpg with a population standard 

deviation of 0.8. The fuel mileages are normally distributed. A random sample was taken 

after the converters were installed and the following data were recorded for fuel mileage. 

Check the sample for outliers and remove any outliers before performing the test. 

 7.2 7.6 7.9 7.1 7.6 7.3 7.3 7.2 7.0 7.3 7.5 7.0 

A) (2 point) State the claim and the alternate hypothesis (H1) ( ≠μ0; <μ0; >μ0 ) 

 

 

B) (2 point) What type of test used to evaluate the owner’s claim (z-Test or t-Test)? 

 

 

C) (4 points) With an  = 0.10, is the fuel mileage higher with the new converters? 

 What is the p-value? 

 

 

 Do you Reject the Null Hypothesis or Not Reject the Null Hypothesis? 

 State the result (whether the data supports the claim or not). 

 

 

 

 

 

 

4. (2 points Extra Credit) Referring the information from Problem #3 above, how much lower 

or higher would the sample mean have to be for you to reverse the decision you made in 

Problem #3? That is, if you rejected the null hypothesis with a sample mean of 7.33, how 

small a value of the sample mean would it take for you to just barely NOT reject the null 

hypothesis? Conversely, if you did NOT reject the null in Problem #3, how large a value of 

the sample mean would it take for you to just barely reject the null hypothesis? Round you 

answer to three decimal places (e.g. 1.234). 

 

 

 

 

 

 Homework Assignment #8 – Intro to Statistics – MTH115 – Spring 2014

Page 3 

5. A nutritionist believes that children under the age of 10 are consuming too much sodium, 

more than the USDA recommended allowance of 2400mg. She takes a sample of 24 

children and measures the sample mean for sodium consumption to be 2642mg with a 

sample standard deviation of 1222. Based on this sample, can the nutritionist claim that 

children are consuming too much sodium? Assume the data are normally distributed. 

A) (2 point) State the claim and the alternate hypothesis (H1) ( ≠μ0; <μ0; >μ0 ) 

 

 

B) (2 point) What type of test used to evaluate the nutritionist’s claim (z-Test or t-Test)? 

 

C) (4 points) With an  = 0.05 can it be concluded that children are consuming more than 

 the recommended allowance? 

 What is the p-value? 

 

 

 Do you Reject the Null Hypothesis or Not Reject the Null Hypothesis? 

 State the result (whether the data supports the claim or not). 

 

 

 

 

6. The national average for core body temperature is 98.0 degrees Fahrenheit. A researcher 

from Wisconsin thinks the average in his state is different (either higher or lower). He takes 

the following random sample of people in Wisconsin to test this claim. Assume the data are 

normally distributed. Do the data support the researcher’s claim? Check the sample for 

outliers and remove any outliers before performing the test. 

 99.1 97.3 98.1 97.4 98.5 98.5 97.6 98.4 96.9 96.9 

 97.8 98.1 98.5 98.6 97.8 97.3 98.3 98.4 98.6 98.4 

 98.7 98.6 98.5 100.2 97.3 97.9 99.1 98.1 99.7 97.2 

A) (2 points) State the claim and the alternate hypothesis (H1) ( ≠μ0; <μ0; >μ0 ) 

 

 

B) (2 points) What type of test used to evaluate the claim (z-Test or t-Test)? 

 

C) (4 points) With an  = 0.05, are the core body temperatures in Wisconsin different 

 from the national average? 

 What is the p-value? 

 

 

 Do you Reject the Null Hypothesis or Not Reject the Null Hypothesis? 

 State the result (whether the data supports the claim or not). 

 

 

 

 

Subject Mathematics
Due By (Pacific Time) 04/20/2014 07:00 pm
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