Answer:
Second option {x | x > 7}
Step-by-step explanation:
We have the function
We know that the square root of a negative number has no solution in the real ones. Therefore the domain of this function is
When applying the transformation:
we have a translation of the original function in 7 units to the right and 2 units to the top:
In the same way we must guarantee that
Then .
Therefore the domain of f(x) is {x | x > 7}
Answer:
We conclude that the sample is from a population of songs with a mean greater than 210 seconds.
Step-by-step explanation:
We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.
Assume that the standard deviation of song lengths is 54.5 sec.
Let = <u><em>population mean length of the songs</em></u>
So, Null Hypothesis, :
210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}
Alternate Hypothesis, :
> 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}
The test statistics that will be used here is <u>One-sample z-test statistics </u>because we know about population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean length of songs = 252.5 seconds
= population standard deviation = 54.5 seconds
n = sample of current hit songs = 40
So, <u><em>the test statistics</em></u> =
= 4.932
The value of z-test statistics is 4.932.
Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.
Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.