Respuesta :
Answer:
The correct test statistic for the hypothesis test is [tex]t = -1.87[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 16[/tex]
The alternate hypotesis is:
[tex]H_{1} < 16[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
In this question:
[tex]X = 15.6, \mu = 16, s = 0.8, n = 14[/tex]
So
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{15.6 - 16}{\frac{0.8}{\sqrt{14}}}[/tex]
[tex]t = -1.87[/tex]
The correct test statistic for the hypothesis test is [tex]t = -1.87[/tex]
Hypothesis test used to check the results of the experiments gives true for the meaningful results.. The correct test statistic for the hypothesis test is -1.871.
Given information-
The mean battery life of the laptop is 16 hours claimed by the company.
The random sample for the test is 14.
Average life of the batteries found out as 15.6 hours.
The deviation for this result is 0.8 hours.
What is hypothesis test?
Hypothesis test used to check the results of the experiments gives true for the meaningful results.
As the mean battery life of the laptop is 16 hours claimed by the company.The null hypothesis for the given problem is,
[tex]H_o\mu=16[/tex]
As average life of the batteries found out as 15.6 hours. Thus the alternate hypothesis for the given problem is,
[tex]H_1\mu<16[/tex]
One sample t test can be found using the below formula,
[tex]t=\dfrac{\overline x -\mu_o}{\dfrac{s}{\sqrt{n} } }[/tex]
Here, [tex]\overline x[/tex] is mean value, [tex]n[/tex] is the number of random sample and [tex]s[/tex] is the deviation.
Put the values,
[tex]t=\dfrac{15.6 -16}{\dfrac{0.8}{\sqrt{14} } }\\t=-1.871[/tex]
Thus the correct test statistic for the hypothesis test is -1.871.
Learn more about the hypothesis here;
https://brainly.com/question/2695653
