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In order to conduct a hypothesis test of the population mean, a random sample of 24 observations is drawn from…

Daniel Kevins

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In order to conduct a hypothesis test of the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 4.8 and 0.8, respectively. Use Table 2.

 

Use the p-value approach to conduct the following tests at α = 0.05.

 

H0: μ ≤ 4.5 against HA: μ > 4.5

 

a-1.

Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

 

  Test statistic    

  
  b.  x = 110; n = 300       
  c.  formula225.mml = 0.34; n = 50       
  d.  formula226.mml = 0.34; n = 400       
 

 

 

The margarita is one of the most common tequila-based cocktails, made with tequila mixed with triple sec and lime or lemon juice, often served with salt on the glass rim. A common ratio for a margarita is 2:1:1, which includes 50% tequila, 25% Triple Sec, and 25% fresh lime or lemon juice. A manager at a local bar is concerned that the bartender does not use the correct proportions in more than 50% of margaritas. He secretly observes the bartender and finds that he used the correct proportions in only 10 out of 30 margaritas. Use the critical value approach to test if the manager’s suspicion is justified at α = 0.05. Let prepresent incorrectly used proportions. Use Table 1.
 
a.

Select the null and the alternative hypotheses.
   
 
[removed] H0: p ≤ 0.50; HA: p > 0.50
[removed] H0: p ≥ 0.50; HA: p < 0.50
[removed] H0: p = 0.50; HA: p ≠ 0.50

 

b.

Calculate the sample proportion. (Round your answer to 3 decimal places.)

 

  Sample proportion [removed]  

 

c.

Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

 

  Test statistic [removed]  

 

d.

Calculate the critical value. (Round your answer to 2 decimal places.)

 

  Critical value [removed]  

 

e.

What is the conclusion?
   
 
[removed] The manager’s suspicion is justified since the value of the test statistic falls in the rejection region.
[removed] The manager’s suspicion is not justified since the value of the test statistic falls in the rejection region.
[removed] The manager’s suspicion is justified since the value of the test statistic does not fall in the rejection region.
[removed] The manager’s suspicion is not justified since the value of the test statistic does not fall in the rejection region.

New research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo.com, July 23, 2008). Even web-savvy surfers could find themselves the victims of identity theft because they have been conditioned to ignore potential signs about whether the banking site they are visiting is real or a bogus site served up by hackers. Researchers at the University of Michigan found design flaws in 78% of the 214 U.S. financial institution websites they studied. Is the above sample evidence sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud? Use a 5% significance level for the test.
 
a.

Select the null and the alternative hypotheses.
   
 
[removed] H0: p ≥ 0.75; HA: p < 0.75
[removed] H0: p ≤ 0.75; HA: p > 0.75
[removed] H0: p = 0.75; HA: p ≠ 0.75

b.

Calculate the sample proportion. (Round your answer to 2 decimal places.)

 

  Sample proportion [removed]  

c.

Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

 

  Test statistic [removed]  

 

d.

Calculate the p-value of the test statistic.(Round your intermediate calculations to 4 decimal places. Round “z” value to 2 decimal places and final answer to 4 decimal places.)

 

  p-value [removed]  

 

e.

What is the conclusion?
   
 
[removed] Reject H0; more than 75% of banking facilities are prone to fraud.
[removed] Reject H0; more than 75% of banking facilities are not prone to fraud.
[removed] Do not reject H0; more than 75% of banking facilities are prone to fraud.
[removed]

Do not reject H0; more than 75% of banking facilities are not prone to fraud.

A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 20 minutes. A sample of 32 main roads results in a mean waiting time of 22.08 minutes with a standard deviation of 5.42 minutes. Use Table 2.

 

a. Select the relevant null and the alternative hypotheses.
   
 
[removed] H0: μ ≤ 20; HA: μ > 20
[removed] H0: μ = 20; HA: μ ≠ 20
[removed] H0: μ ≥ 20; HA: μ < 20

 

b.

Compute the value of the appropriate test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

 

  Test statistic [removed]  

 

c-1.

Calculate the critical value at a 1% level of significance. (Round your answer to 3 decimal places.)

 

  Critical value [removed]  

 

c-2.

Determine whether or not the city should increase its transportation budget.
   
 
[removed] Reject H0; the city should increase its transportation budget
[removed] Do not reject H0; the city should increase its transportation budget
[removed] Reject H0; the city should not increase its transportation budget
[removed]

Do not reject H0; the city should not increase its transportation budget

 

 

An investor wants to test whether the average return of Vanguard’s Precious Metals and Mining Fund is greater than 12% based on data over the past 25 years. Assume returns are normally distributed with a population standard deviation of 30%.

 

PictureClick here for the Excel Data File

 

a. Select the null and the alternative hypotheses for the test.
   
 
[removed] H0: μ ≥ 12; HA: μ < 12
[removed] H0: μ = 12; HA: μ ≠ 12
[removed] H0: μ ≤ 12; HA: μ > 12

 

b.

Use the Excel function Z.TEST to calculate the p-value. (Round your answer to 4 decimal places.)

 

  p-value [removed]  

 

c. At α = 0.05, what is the conclusion?
   
 
[removed] Reject H0 since the p-value is smaller than α.
[removed] Reject H0 since the p-value is greater than α.
[removed] Do not reject H0 since the p-value is smaller than α.
[removed] Do not reject H0 since the p-value is greater than α.

 

d. Is the return on Vanguard’s Precious Metals and Mining Fund greater than 12%?
   
 
[removed] No
[removed] Yes

 

 

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