Respuesta :
Answer:
a)Null hypothesis:[tex]\mu=35.1[/tex]
Alternative hypothesis:[tex]\mu \neq 35.1[/tex]
b) The 95% confidence interval would be given by (27.131;34.669)
c) Since the confidence interval contains the value of interest 35.1 we don't have enough evidence to reject the null hypothesis at 5% of significance.
Step-by-step explanation:
Data given and notation
[tex]\bar X=30.9[/tex] represent the sample mean
s=11.8 represent the sample deviation
n=40 sample size
Confidence =0.95 or 95%
Part a
On this case the correct system of hypothesis would be:
Null hypothesis:[tex]\mu=35.1[/tex]
Alternative hypothesis:[tex]\mu \neq 35.1[/tex]
Part b
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=40-1=39[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,39)".And we see that [tex]t_{\alpha/2}=2.02[/tex]
Now we have everything in order to replace into formula (1):
[tex]30.9-2.02\frac{11.8}{\sqrt{40}}=27.131[/tex]
[tex]30.9-2.02\frac{11.8}{\sqrt{40}}=34.669[/tex]
So on this case the 95% confidence interval would be given by (27.131;34.669)
Part c
(c) Determine if the researcher will reject the null hypothesis.
Since the confidence interval contains the value of interest 35.1 we don't have enough evidence to reject the null hypothesis at 5% of significance.
