Significance tests a test of h0: p = 0.65 against ha: p < 0.65 has test statistic z = −1.78. (a) what conclusion would you draw at the 5% significance level? at the 1% level? (b) if the alternative hypothesis were ha: p ≠ 0.65, what conclusion would you draw at the 5% significance level? at the 1% level?

(a) At 5% significance level, reject H0

At 1% significance level, reject H0

(b) At 5% significance level, fail to reject H0

At 1% significance level, fail to reject H0

Step-by-step explanation:

(a) The test is a one tailed test

At 5% significance level, the critical value is 1.645

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645

At 1% significance level, the critical value is 2.326

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326

(b) The test is a two tailed test

At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96

Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96

At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576

Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.