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Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is less than 63 gallons per day at 1% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is less than 63, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(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".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one side lower test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is less than 63 gallons per day at 1% of signficance.
Answer:
Null hypothesis:
Alternative hypothesis:
Since is a left tailed test the p value would be:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
Be Careful with the system of hypothesis!
If we conduct the test with the following hypothesis:
Null hypothesis:
Alternative hypothesis:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis.
Step-by-step explanation:
1) Data given and notation
n=110 represent the random sample taken
X=97 represent the students who completed the modules before class
estimated proportion of students who completed the modules before class
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
Be Careful with the system of hypothesis!
If we conduct the test with the following hypothesis:
Null hypothesis:
Alternative hypothesis:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis.
