Question

Students conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 330 spins, 180 landed with the heads side up (a) Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads up is not 0.5? Test the relevant hypotheses using α decimal places.) 0.01. (Round your test statistic to two decimal places and your P-value to four P-value - State your conclusion ๏ Do not reject Ho, we do not have convincing evidence that the proportion of the time this type of coin lands heads up is not 0.5 Reject Ho. We have convincing evidence that the proportion of the time this type of coin lands heads up is not 0.5 O Reject Ho. We do not have convincing evidence that the proportion of the time this type of coin lands heads up is not 0.5 O Do not reject H. We have convincing evidence that the proportion of the time this type of coin lands heads up is not 0.5 0" (b) Would your conclusion be different if a significance level of 0.05 had been used? Explain O Yes. With a significance level of 0.05, the conclusion would be different, since the P-value is greater than 0.05 ๏ No, with a significance level of 0.05, the conclusion would be the same, since the P-value is greater than 0.05 O Yes. With a significance level of 0.05, the conclusion would be different, since the P-value is less than 0.05 O No. With a significance level of 0.05, the conclusion would be the same, since the P-value is less than 0.05 You may need to use the appropriate table in Appendix A to answer this question Need Help?Read It Talk to a Tutor 1/3 points| Previous Answers PODStat5 10.E.080 My Notes Ask Your Teacher An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test. Six nonprofessional drivers were selected, and each one drove a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles per gallon) are given below 27.3 29.2 31.2 28.3 30.2 29.6 Assuming that fuel efficiency is normally distributed under these circumstances, do the data contradict the claim that true average fuel efficiency is (at least) 30 mpg? Test the appropriate hypotheses at significance level 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) P-value -

Answer 1

Ho :   µ =   30                  
Ha :   µ <   30       (Left tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   1.3799                  
Sample Size ,   n =    6                  
Sample Mean,    x̅ = ΣX/n =    29.3                  
              
degree of freedom=   DF=n-1=   5                  
                          
Standard Error , SE = s/√n =   1.3799   / √    6   =   0.563      
t-test statistic, t = (x̅ - µ )/SE = (   29.300   -   30   ) /    0.563   =   -1.24
                          
  
p-Value   =   0.1346 [Excel formula =t.dist(t-stat,df) ]