Two mixed numbers with different denominators to get 4 1/3
1 answer:
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Answer:
So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:
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 (variable of interest)
represent the population standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:
Using the t-distribution, as we have the standard deviation for the samples, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the treatment increases the survival time of patients.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, we test if the treatment did not increase the survival time, that is, the subtraction of means is 0, hence:
At the alternative hypothesis, we test if the treatment has increased the survival time, hence:
For each sample, we have that:
Hence, for the distribution of differences, the mean and the standard error are given by:
It is given by:
In which is the value tested at the null hypothesis.
Hence:
Considering a<em> right-tailed test</em>, as we are testing if the mean is greater than a value, with a <em>standard significance level of 0.05 and 8 + 8 - 2 = 14 df</em>, we have that the critical value is of .
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the treatment increases the survival time of patients.
More can be learned about the t-distribution at brainly.com/question/13873630