MATH SOLVE

3 months ago

Q:
# 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

A:

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]