What is 783 divided by 18
2 answers:
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Answer:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
represent the sample mean for the sample
population mean
s=4.0 represent the sample standard deviation
n=64 represent the sample size
Assuming the X follows a normal distribution
The sample mean have the following distribution:
The margin of error for the sample mean is given by this formula:
Since we have the sample standard deviation we can estimate the margin of error like this:
The next step would be find the value of ,
and
We can find the degrees of freedom like this:
And we can find the critical value with the following code in excel for example: "=T.INV(0.025,63)" and we got:
And the margin of error would be :
Answer:
a)
b) We are uncertain
c) It will change significantly
Step-by-step explanation:
a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.
Since we assume that the variances are equal, we use the pooled variance given as
,
where .
The mean difference .
The confidence interval is
b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.
c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.