A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some de
1 answer:
Yes at 0.05 significance level we can conclude that mean income of those selecting plan B is bigger.
Given mean yearly income for sample of 40 subscribers is $57000 with standard deviation of $9200, mean yearly income for sample of 30 subscribers with standard deviation of $7100.
First we have been given significance level (α) of 0.05. So (1-α)=1-0.05=0.95 and we have to find Z score for this significance level. (1+0.95)/2=0.425
Z=1.44
Now we have to calculate margin of error which will be calculated as under:
=
=1.44*9200/6.32
=1869.10
=
=1.44*7100/3.47=2096.2
We know that margin of error shows the difference between real and calculated values. So if we increase mean of both plans by margin of error of respective plans then mean of plan A becomes=57000+1869.10=58869.10 and mean of plan B becomes =61000+2096.2=630622.2. We can clearly notice that mean of plan B is greater.
Hence it is reasonable to say that the mean of plan B is greater at the significance level of 0.05.
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Answer:
a)
And we can find this probability using the normal standard table or excel:
b)
And we can find this probability using the complement rule and the normal standard table or excel:
c)
And we can find this probability with this difference:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the life of a particular brand of a population, and for this case we know the distribution for X is given by:
Where and
Part a
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel:
Part b
And we can find this probability using the complement rule and the normal standard table or excel:
Part c
For this case we select a sample size of n =16. and we want this probability:
We know that the distribution for the sample mean is given by:
And we can find the z scores for the limits like this:
And we can find this probability with this difference: