A tailor designed three pairs of pants (P1, P2, and P3) and five tops (T1, T2, T3, T4, and T5) to create outfits. How many diffe
rent outfits can the tailor create? Consider making a tree diagram or a table to help find the answer.
The tailor can create___ outfits.
The tailor can create___ outfits.
1 answer:
Answer:
15 outfits
Step-by-step explanation:
We have 3 possibilities for pants and 5 possibilities for tops.
The tailor has 3 possible pants to choose from and 5 possible tops to choose from. Using the Fundamental Counting Principle, we can simply multiply these two together to get the total number of possible outfits:
3 * 5 = 15 outfits
Or, we could make a tree diagram. See attachment. It will give the same answer.
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Answer:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: 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, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0
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 mean is lower than 20, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but 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:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: 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, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0