the sine function is a many-to-one function and therefore has no inverse function.
However if the domain is restricted to -90° ≤ x ≤ 90°
Then the function is one-to-one for this domain
Thus, x is defined as the angle such that - π/2 ≤ x ≤ π/2
5π/6 is therefore outwith the domain
Answer:
Step-by-step explanation:
Data given and notation
represent the average score for the sample
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a two tailed test.
What are H0 and Ha for this study?
Null hypothesis:
Alternative hypothesis :
Compute the test statistic
The sample size is large enough to assume the distribution for the statisitc normal. The statistic for this case is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
We can replace in formula (1) the info given like this:
Give the appropriate conclusion for the test
Since is a two tailed test the p value would be:
Conclusion
If we compare the p value and a significance level given for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, then the true population mean for the salary not differs significantly from the value of 39000.