Week 4 Practice Set

  1. Find z for each of the following confidence levels. Round to two decimal places.
Question Answer
a. 90%  
b. 95%  
c. 99%  

 

  1. For a data set obtained from a random sample, n = 81, x = 48.25, and σ = 4.8.

 

Question Answer
a. What is the point estimate of μ? Round to two decimal places.  
b. Calculate a 95% confidence interval for μ.What are the lower and upper limits? Round to two decimal places. Lower

Upper

c. What is the margin of error? Round to two decimal places.  

 

  1. Determine the sample size needed to estimate μ for the following.
Question Answer
a. E = 2.3,  σ = 15.40, confidence level = 99%. Round to the nearest whole number.  
b. E = 4.1,  σ = 23.45, confidence level = 95%. Round to the nearest whole number.  
c. E = 25.9,  σ = 122.25, confidence level = 90%. Round to the nearest whole number.  

 

 

 

  1. Are these claims about hypothesis testing True or False?
Question Answer
a. The null hypothesis is a claim about a population parameter that is assumed to be false until it is declared false.  
b. An alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is false.  
c. The significance level, denoted by α, is the probability of making a Type II error, that is, the probability of rejecting the null hypothesis when it is actually true.  
d. The nonrejection region is the area to the right or left of the critical point where the null hypothesis is not rejected.  
e. Thelevelofsignificanceinatestofhypothesisistheprobabilityofmakinga Type III error.ItistheareaundertheprobabilitydistributioncurvewherewerejectHo.  

 

  1. The following information is obtained from two independent samples selected from two populations.

n1 =650         ¯x1 =1.05       σ1 =5.22

n2 =675         ¯x2 =1.54       σ2 =6.80

Question Answer
a. In selecting which version of the z/t test of means to use, consider the sample size and whether you are given the population or sample standard deviations. Given the data above, will you use a z or t test?  
b. What is the value of z? Round to two decimal places.  
c. Would you reject the null hypothesis? YES or NO  

 

  1. Using data from the U.S. Census Bureau and other sources, www.nerdwallet.com estimated that considering only the households with credit card debts, the average credit card debt for U.S. households was $15,523 in 2014 and $15,242 in 2013. Suppose that these estimates were based on random samples of 600 households with credit card debts in 2014 and 700 households with credit card debts in 2013. Suppose that the sample standard deviations for these two samples were $3870 and $3764, respectively. Assume that the standard deviations for the two populations are unknown but equal.
Question Answer
a. Let μ1 and μ2 be the average credit card debts for all such households for the years 2014 and 2013, respectively. What is the point estimate of μ1 − μ2? Round to two decimal places. Do not include the dollar sign.  
b. Construct a 98% confidence interval for μ1 − μ2. Do not include the dollar sign. What are the lower and upper bounds? Round to two decimal places. Lower

Upper

c. Using a 1% significance level, can you conclude that the average credit card debt for such households was higher in 2014 than in 2013? Use both the p-value and the critical-value approaches to make this test.

Reject Ho      OR      Do not reject Ho

 

 

  1. Gamma Corporation is considering the installation of governors on cars driven by itssales staff. These devices would limit the car speeds to a preset level, which is expected to improve fuel economy. The company is planning to test several cars for fuel consumption without governors for 1 week. Then governors would be installed in the same cars, and fuel consumption will be monitored for another week. (Note that this is an example of a paired comparison as each car is operated with and without a governor.)

 

Gamma Corporation wants to estimate the mean difference in fuel consumption with a margin of error of 2 mpg at the 95% confidence level.Assume that the differences in fuel consumption are normally distributed. Previous studies suggest that 3 mpg is a reasonable estimate of the standard deviation. Use this formula to determine the sample size: n = z2 σ2/E2(example 8-3, p. 321).

 

 

Question Answer
How many cars should be tested? Round up to the next whole number.  
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