Which of the following are continuous functions? (Select all that apply.) The temperature at a specific location as a function o
1 answer:
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Answer:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of respondents that trust these labels is not significanlty less than 0.5 or 50%.
Step-by-step explanation:
1) Data given and notation
n=1000 represent the random sample taken
X=498 represent the adults that trust these labels
estimated proportion of respondents that trust these labels
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion of respondents that trust these labels is at least 50%:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level is not provided but we can assume it as . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of respondents that trust these labels is not significanlty less than 0.5 or 50%.
Answer:
a)
And rounded up we have that n=2401
b)
And rounded up we have that n=626
And we see that if we have previous info about p the sample size varies a lot.
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".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
Part a
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
Since we don't have prior information about the population proportion we can use ase estimator . And replacing into equation (b) the values from part a we got:
And rounded up we have that n=2401
Part b
For thi case the estimator for p is
And rounded up we have that n=626
And we see that if we have previous info about p the sample size varies a lot.