Respuesta :
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]
To test DullCo's hypothesis, the p-value is 0.041815 and this can be determined by using the given data.
Given :
- 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.
The following steps can be used in order to determine the p-value for DullCo's hypothesis:
Step 1 - The formula for t-statistics can be used in order to determine the p-value for DullCo's hypothesis.
Step 2 - The formula for t-statistics is given below:
[tex]t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n} }}[/tex]
where the sample size is 'n', the standard deviation is [tex]\sigma[/tex], and the mean is [tex]\mu[/tex].
Step 3 - Now, substitute the values of [tex]\sigma[/tex], [tex]\mu[/tex], [tex]\bar{x}[/tex], and n in the above formula.
[tex]t = \dfrac{37.8-40}{\dfrac{5.4}{\sqrt{18} }}[/tex]
Step 4 - SImplify the above expression.
[tex]t = \dfrac{-2.2}{1.2727}[/tex]
[tex]t = -1.73[/tex]
Step 5 - Now, with the help of the z-table the p-value is:
[tex]\rm p-value = P(Z<-1.73)[/tex]
[tex]\rm p-value = 0.041815[/tex]
To test DullCo's hypothesis, the p-value is 0.041815.
For more information, refer to the link given below:
https://brainly.com/question/14723549
