Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:Select one:a. -2.101b. -1.980c. -1.960d. -1.728

Accepted Solution

Answer:The value is  [tex]p- value  = 0.041815[/tex]Step-by-step explanation:From the question we are told that   The  population mean is [tex]\mu  =  40 \ hours[/tex]   The  sample size is  [tex]n  =  18[/tex]     The  sample mean is  [tex]\= x =  37.8 \ hours[/tex]    The standard deviation is  [tex]\sigma  = 5.4\ hours[/tex]The null hypothesis is  [tex]H_o  :  \mu =  \ge 40[/tex]The alternative hypothesis is  [tex]H_a  :  \mu < 40 \ hour s[/tex]Generally the test statistic is mathematically evaluated as        [tex]t=  \frac{\= x - \mu}{ \frac{\sigma}{ \sqrt{n} } }[/tex]       [tex]t=  \frac{37.8 - 40}{ \frac{5.4}{ \sqrt{18 } }[/tex]       [tex]t=  -1.73[/tex]From the z - table the p-value is obtained and the value is         [tex]p- value  =  P(Z <  -1.73)[/tex]         [tex]p- value  = 0.041815[/tex]