Respuesta :
Answer:
1) Random: A random sample needs to be obtained in order to apply inference for the mean
2) Normality condition: The sampling distribution of [tex]\bar X[/tex] needs to be approximately normal. If we use a random sample size higher than 30 we can use the Central Limit theorem to verify this condition.
3) Independence: All the individual observations need to be independent. And we need to satisfy that our sample would be lower than 10% of the real population size.
Step-by-step explanation:
For this case we need three conditions:
1) Random: A random sample needs to be obtained in order to apply inference for the mean
2) Normality condition: The sampling distribution of [tex]\bar X[/tex] needs to be approximately normal. If we use a random sample size higher than 30 we can use the Central Limit theorem to verify this condition.
3) Independence: All the individual observations need to be independent. And we need to satisfy that our sample would be lower than 10% of the real population size.
Data given and notation
[tex]\bar X=203[/tex] represent the sample mean
[tex]s=10.9[/tex] represent the sample standard deviation
[tex]n=17[/tex] sample size
[tex]\mu_o [/tex] represent the value that we want to test
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We can assume the following system of hypothesis.
Null hypothesis: [tex]\mu = \mu_o[/tex]
Alternative hypothesis :[tex]\mu\neq \mu_o[/tex]
The degrees of freedom on this case:
[tex]df=n-1=10-1[/tex]
Compute the test statistic
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
