Twelve different video games showing drug usedrug use were observed. The duration times of drug usedrug use were recorded, with
1 answer:
Answer:
a) The confidence level is 95%.
b) If the confidence interval, in seconds, is (4.0, 202.2) and the claim is that the population mean is greater than 90 seconds, we conclude that there is no enough evidence for that claim.
Step-by-step explanation:
a) If the hypothesis test is performed with a significance level of α=0.05, the confidence level that corresponds to this significance level is 95%:
If the confidence interval, in seconds, is (4.0, 202.2) and the claim is that the population mean is greater than 90 seconds, we conclude that there is no enough evidence for that claim.
The reason is that, with this confidence level, the confidence interval includes values that are below 90 seconds.
To have evidence to support that claim, the lower bound of the interval shouold have been greater than 90 seconds.
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Answer:
a)
b) For this case we need to find a critical value that accumulates of the area on each tail, we know that
, so then
, using the normal standard table or excel we see that:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.
Step-by-step explanation:
Data given and notation
n=420+174=594 represent the random sample taken
X=174 represent the number of yellow peas
estimated proportion of yellow peas
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:
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
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
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 provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis.
b) Critical value
For this case we need to find a critical value that accumulates of the area on each tail, we know that
, so then
, using the normal standard table or excel we see that:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.