Respuesta :
Answer:
[tex]t=\frac{11.5-10}{\frac{4.5}{\sqrt{100}}}=3.333[/tex]
Critical value
The significance is 5% so then [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] then the critical value for this case would be [tex] z_{\alpha/2}= 1.64[/tex]. Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is higher than 10 mg
P value
The p value would be given
[tex]p_v =P(z>3.333)=0.000434[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 10 mg
Step-by-step explanation:
Information given
[tex]\bar X=11.5[/tex] represent the sample mean
[tex]\sigma=4.5[/tex] represent the population standard deviation
[tex]n=100[/tex] sample size
[tex]\mu_o =10[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 10mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 10[/tex]
Alternative hypothesis:[tex]\mu > 10[/tex]
the statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{11.5-10}{\frac{4.5}{\sqrt{100}}}=3.333[/tex]
Critical value
The significance is 5% so then [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] then the critical value for this case would be [tex] z_{\alpha/2}= 1.64[/tex]. Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is higher than 10 mg
P value
The p value would be given
[tex]p_v =P(z>3.333)=0.000434[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 10 mg
