The average local cell phone call length was reported to be 2.27 minutes. A rand

Question

The average local cell phone call length was reported to be 2.27 minutes. A random sample of 20 phone calls showed an average of 2.98 minutes in length. At an = 0.05 can it be concluded that the average differs from the population average? Assume that the population is approximately normally distributed with a standard deviation of 0.98 minute. Please show work.

a) State the null and alternative hypothesis. b) Select the distribution to use. c) Write the decision rule. (Define the rejection region.) d) Calculate the test statistic. e) Calculate the p-value. f) Make a decision. g) State the type I and II error in context of the problem.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   2.27  
Ha:    u   =/   2.27  

**********************

b)

As sigma = 0.98 is known, and the population is approximately normally distributed, we use z distribution.   [ANSWER]          

**********************

c)

As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.959963985      

Hence, we reject Ho when z < -1.96 or z > 1.96. [ANSWER]

**********************

d)
              
Getting the test statistic, as              
              
X = sample mean =    2.98          
uo = hypothesized mean =    2.27          
n = sample size =    20          
s = standard deviation =    0.98          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.240016865 [ANSWER, TEST STATISTIC]

***********************

e)          
              
Also, the p value is              
              
p =    0.001195226   [ANSWER]

************************

f)

As P < 0.05, we reject Ho.

There is significant evidence at 0.05 level that the population average in which this sample is obtained differs from 2.27 minutes. [CONCLUSION]

**********************

G)

A type I error is concluding that the true mean differs from 2.27 minutes, when i fact, the true mean is 2.27 minutes.      

A type I error is concluding that the true mean is 2.27 minutes, when i fact, the true mean differs from 2.27 minutes.              

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.