Will give brainiest!!! Rose has no more than $65 to spend on girl scout cookies. She has already spent $38.50 on samoas; if thin
2 answers:
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The GCF of 18 and 36 is 18. To solve this, use the picture attached. After creating the boxes, find a number that both 18 and 36 can be divided by, for example, 9. Now that you have 9, divide both 18 and 36 by 9. That equals 2 and 4. Place the numbers underneath the boxes you made previously and find another number that both 2 and 4 are divisible by. 2 and 4 are both able to be divided into 2. Do 2 divided by 2 and 4 divided by 2. Now you have the numbers 1 and 2. There aren't any numbers that can be divided into 1 and 2, so now you are left with the numbers 9 and 2. Multiply the numbers together to get a GCF of 18. Hope this helped!
Answer:
(B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.
(C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours.
Step-by-step explanation:
1) Data given and notation
represent the battery life 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)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean battery life is less than 20 :
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviation, 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".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) P-value
First we need to calculate the degrees of freedom given by:
Since is a one-side lower test the p value would be:
5) 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 to reject the null hypothesis, so we can conclude that the average battery life it's not significantly different less than 20 hours at 5% of signficance. If we analyze the options given we have:
(A) Reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours. FALSE, we FAIL to reject the null hypothesis.
(B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours. TRUE, we fail to reject the null hypothesis that the mean would be 20 or higher .
(C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours. TRUE, we FAIL to reject the null hypothesis that the mean is greater or equal to 20 hours, so we reject the alternative hypothesis that the mean is less than 20 hours.
(D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean battery life of the smartphone is not equal to 20 hours. FALSE the claim is not that the mean is different from 20. The real claim is: "Javier believes the mean battery life is less than 20 hours".