[2x(3+5)+6]x4 what is the value of this expression
2 answers:
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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 probability that the plane is oveloaded is P=0.9983.
The pilot should take out the baggage and send it in another plain or have less passengers in the plain to not overload.
Step-by-step explanation:
The aircraft will be overloaded if the mean weight of the passengers is greater than 163 lb.
If the plane is full, we have 41 men in the plane. This is our sample size.
The weights of men are normally distributed with a mean of 180.5 lb and a standard deviation of 38.2.
So the mean of the sample is 180.5 lb (equal to the population mean).
The standard deviation is:
Then, we can calculate the z value for x=163 lb.
The probability that the mean weight of the men in the airplane is below 163 lb is P=0.0017
Then the probability that the plane is oveloaded is P=0.9983:
The pilot should take out the baggage or have less passengers in the plain to not overload.