Respuesta :
Answer:
a) Null hypothesis:[tex]\mu \geq 3[/tex]
Alternative hypothesis:[tex]\mu < 3[/tex]
This hypothesis test is a left tailed test.
b) [tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =P(z<-2.784)=0.0027[/tex]
We can conduct the test with the Ti84 using the following steps:
STAT>TESTS>T-test>Stats
We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.
And we got the same results.
Step-by-step explanation:
Information given
[tex]\bar X=2.8[/tex] represent the sample mean
[tex]s=2.6[/tex] represent the population standard deviation
[tex]n=1310[/tex] sample size
[tex]\mu_o =3[/tex] represent the value to test
[tex]\alpha=0.5[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Part a) System of hypothesis
We want to test if the true mean is less than 3, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 3[/tex]
Alternative hypothesis:[tex]\mu < 3[/tex]
This hypothesis test is a left tailed test.
Part b
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =P(z<-2.784)=0.0027[/tex]
We can conduct the test with the Ti84 using the following steps:
STAT>TESTS>T-test>Stats
We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.
And we got the same results.
