Solve the equation 2/7=6x/4x+17
2 answers:
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Answer:
We see that the p value is lower than the significance level given of 0.01 so then we can conclude that the true mean for the nicotine content is significantly higher than 40 mg
Step-by-step explanation:
Information provided
represent the average nicotine content
represent the sample standard deviation
sample size
represent the value to check
represent the significance level for the hypothesis test.
t would represent the statistic
represent the p value for the test
System of hypothesis
We want to verify if the nicotine content of the cigarettes exceeds 40 mg , the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic for this case would be:
(1)
And replcing we got:
The degrees of freedom are:
The p value would be:
We see that the p value is lower than the significance level given of 0.01 so then we can conclude that the true mean for the nicotine content is significantly higher than 40 mg
Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.
<h3>What does the Central Limit Theorem state?</h3>- It states that the sampling distribution of sample means of size n has standard deviation
.
- By the Empirical Rule, 95% of the sample means fall within 2 standard errors of the mean.
In this problem, we have that the standard deviation and the sample size are given as follows:
Hence the standard error is given by:
[tex]s = \frac{10.34}{\sqrt{400}} = 0.517.
Two standard errors is represented by:
2 x 0.517 = $1.034.
Hence, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.
More can be learned about the Central Limit Theorem at brainly.com/question/24663213
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