Calculations Shown



1. What is the appropriate critical value for each of the following confidence levels and sample sizes? (Remember that in regard to confidence level this implies two-tails) 
  
(a) Critical z-value for an 95% confidence level for sample of size n= 65:  
      
      
2 How do you know when to use a t-distribution and associated critical t-values as opposed to a z-distribution and critical z-values within a confidence interval or hypothesis testing situation? 
  
      
3. Apple iPad engineers would like to know the mean time for movie downloads. They calculated the download time for a specific movie by 24 randomly selected iPads, and the data is shown to the right.  
   Download time of Apple iPads (in seconds)
 (a) Determine the mean and standard deviation of this sample data.  23
 (b) Determine the expected margin of error amount in using this sample result to estimate the mean download time for this same movie of all Apple iPads based upon a 95% desired level of confidence.    Std. Dev. =
 (c) Determine the 95% confidence interval for the mean download time all iPads.   
 (d) State your final confidence interval result in a sentence that interprets the result within the context of the situation.  
   
4. Answer the following: 
(a) What is the meaning of the term “null hypothesis” in statistics. 
      
(b) How do you know when to perform a “left-tailed” test in a hypothesis-testing situation versus a “right-tailed” or “two-tailed” test? 
  
In multiple choice problems 5 and 6, select the best answer.      
5.  A statistical hypothesis test is used to test a claim.  You get 1.96 as the test statistic from the collected sample and a 1.985 as your critical value in a right-tailed test.  Which of the following is the correct decision statement for the test?
A. Fail to reject the null hypothesis 
B. Claim the null hypothesis is true 
C. Reject the null hypothesis 
D. Claim the alternative hypothesis is false 
      
6. A statistical hypothesis test is used to test a claim.  You get a P-value of 0.083 on a test with a significance level of 0.10.  Which of the following is the correct decision statement for the test?
A. Fail to reject the null hypothesis 
B. Claim the null hypothesis is true 
C. Reject the null hypothesis 
D. Claim the alternative hypothesis is false 
      
      
7. The posted speed limit on Interstate 70 near Hays, KS is 75 miles per hour, but it is claimed that the mean of the actual speeds of vehicles is greater than 75 miles per hour. Describe the Type I error you could make if you test this claim through a formal hypothesis test on collected data.  
   
      
8. The posted speed limit on Interstate 70 near Hays, KS is 75 miles per hour, but it is claimed that the mean of the actual speeds of vehicles is greater than 75 miles per hour. To test this claim, the speeds of 36 randomly selected vehicles were taken and then reported to the right.  73
   68
   74
       81
       75
(a) Give the null and alternative hypotheses for this situation in mathematical notation.  84
 (b) Based upon a 10% level of significance, determine the critical value(s) associated with this hypothesis test.  
      
(c) Determine the sample’s test statistic.   
 (d) State a final conclusion regarding the results of the hypothesis test.  Make sure your statement is tied to the context of the problem (speed of vehicles on I-70 near Hays, KS).  
9. A report by the NCAA states that 85% of fans want a larger March Madness Tournament. A local educational expert believes that FHSU college students don’t agree, so he randomly selects 125 FHSU students and finds that 98 want a larger tournament. Follow the steps below to conduct a hypothesis test to determine, at the 5% significance level, if the percentage of students wanting a larger tournament is less than 85%.  
   
(a) List the null and alternative hypotheses for this test.  
 (b) Determine the value of the sample’s test statistic.  
      
(c) Determine the critical value(s).  
 (d) Detemine the P-value.  
 (e) Write a final interpretive sentence tied to the context for the hypothesis test results.
10. Self-reported heights and measured heights of twelve males aged 12 – 16 are shown in the table to the right. At the 5% significance level, is there sufficient evidence to support the claim that there is a difference between the average reported heights and the measured heights of males aged 12 -16? All measurements are in inches. Note: Hypothesis testing method work must be shown for credit on this problem. Reported Height Measured Height
   
  69 67.9
  71 69.9
  64 64.9
  71 68.3
11. At the right, give an example of a paired data set (with at least 5 pairs) that demonstrates a strong (but not perfect) positive linear correlation. x y
      
      
12. Give a real life example of two variables that are likely to be negatively correlated.  Specifically explain why you believe they are negatively correlated.  
   
   
   
   
      
      
13. Suppose some researchers determine that there is a significant strong positive correlation between a student’s GPA and the final exam grade in MATH 250 Elements of Statsitics. From this correlation, can we determine that a student’s GPA is the cause of a high final exam grade in statistics? Explain your answer.  
   
       
       
Use the following situation to answer questions 14 to 18 below: x y
 A criminal laboratory must sometimes estimate a person’s height from partial skeletal remains. A random sample of eight adult male x-rays gave the following information, where x = length of femur (the thigh bone) in inches and y = body height in inches. This information will be used to determine a possible relationship between femur length and height. 17.5 72
14. Produce a scatterplot of this paired data at the right.         
 15. Which of the following best describes the correlation that is demonstrated by the scatterplot (Choose the one best answer.)  
    
 A. No Correlation     
 B. Strong Positive Correlation     
 C.  Strong Negative Correlation     
 D. Correlation, but not linear (A quadratic curve gives a better fit than the linear trendline.)    
    
      
 16. Determine the sample’s correlation coefficient r and the coefficient of determination r2.  Then explain clearly whether or not we should conclude that  the correlation in these two variables is statistically significant.  
    Correlation coefficient
    Coefficient of determination
17. Give the equation of the line-of-best-fit (trend line), the slope of this line, and explain what the slope means in the context of this problem.  
18. What should one predict the height of an adult male to be if femur length is 19.5 inches?  
    y’ = 3.553*19.5 + 9.7548