Jane is buying a carpet for two small rooms. One is a closet that needs 16 Sq Ft of Carpet the other room is a small bedroom if
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Answer:
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).
The null and alternative hypothesis are:
Step-by-step explanation:
<em>The question is incomplete: To test this claim a sample or population standard deviation is needed.</em>
<em>We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.</em>
<em> NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.</em>
This is a hypothesis test for the population mean.
The claim is that the batteries power the laptops for significantly less than 4 hours.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=3.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.
Answer:
The formula to generate 70% confidence interval is: , in which
is the sample mean.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a pvalue of , so Z = 1.037.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz.
This means that .
Sample of 10 birds:
This means that .
The margin of error is of:
The lower end of the interval is the sample mean of subtracted by M.
The upper end of the interval is the sample mean of added to M.
Then, the formula to generate 70% confidence interval is: , in which
is the sample mean.