A coin was flipped 60 times and came up heads 38 times. At the .10 level of significance, is the coin biased toward heads? (a-1) H0: π ≤ .50 versus H1: π > .50. Choose the appropriate decision rule at the .10 level of significance. a. Reject H0 if z >1.282 b. Reject H0 if z < 1.282 a b (a-2) Calculate the test statistic. (Carry out all intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) Test statistic (a-3) The null hypothesis should be rejected. True False (a-4) The true proportion is greater than 0.5. True No evidence to support (b-1) Find the p-value. (Round your answer to 4 decimal places.) p-value (b-2) Is the coin biased toward heads? Yes No

a1) The null and alternative hypothesis are:

Reject H0 if the test statistic is larger than 1.282 (z>1.282)

a2) Test statistic z=1.94

a3) True.

a4) True.

b1) P-value=0.0264

b2) Yes, it is biased towards heads.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the coin is biased towards heads.

Then, the null and alternative hypothesis are:

The significance level is 0.10.

The sample has a size n=60.

The sample proportion is p=0.6333.

The standard error of the proportion is:

Then, we can calculate the z-statistic as:

This test is a right-tailed test, so the P-value for this test is calculated as:

As the P-value (0.0264) is smaller than the significance level (0.10), the effect is  significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that the coin is biased towards heads.

The critical value for a significance level of 0.1 is z=1.282. As this is a right-tailed test, the decision rule is: "Reject H0 if the test statistic is larger than 1.282 (z>1.282)", as the rejection region is for every z over 1.282.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4