Answer:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of songs selectd at random differs from 0.5 .
There is strong evidence that the proportion of songs downloaded by Ted and Suzanne differs from 0.5.
Step-by-step explanation:
Data given and notation
n=30 represent the random sample taken
X=22 represent the number of songs selectd at random
estimated proportion of songs selectd at random
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)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of random songs selected is 0.5 (random) or no.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, 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 assumed for this case is . 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 assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of songs selectd at random differs from 0.5 .
There is strong evidence that the proportion of songs downloaded by Ted and Suzanne differs from 0.5.