A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage for foodservice workers in the U. S. Last year's mean hourly wage was $8.08, and there is reason to believe that this year's value is greater than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has increased. The union chooses a random sample of 100 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U. S. has a standard deviation of $1.18 and that the union performs its hypothesis test using the 0.1 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.(If necessary, consult a list of formulas.)
a. What are the null and alternative hypotheses that the union should use for the test?
b. What is the probability that the union rejects the null hypothesis when, in fact, it is true? Round your response to at least two decimal places.
c. Assuming that the actual value is $8.28, what is the power of the test? Round your response to at least two decimal places.
d. Suppose that the union decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same level of significance, but for this second test the union chooses a random sample of size 75 instead of a random sample of size 100. Assuming that the actual value is $8.28, how does the probability that the union commits a Type II error in this second test compare to the probability that the union commits a Type II error in the original test?

The slope of a line is -1/2 . what is the slope of a line that is parallel to it? a. 1/2 b.2 c. -1/2 d. -2

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Complete the worksheet. use 3.14 for π and round all decimals to the nearest hundredth.find the volume of the composite three-dimensional figure above. important terms are written in bold.1. the pyramid has a square base that is inscribed in the circular base of the cone. draw an image of the composite shape of the base. 2. if the side length of the square base is 8 units long, what is the diameter of the circular base of the cone from the picture in number 1? 3. now that the diameter has been calculated, what is the circular area of the cone? ignore the square base of the pyramid.? 4. what is the formula for volume of a cone? 5.to calculate the volume of the cone, the height is still needed. if the cone has a lateral surface with a length of 13 units, what is the height of the cone? 6.now find the volume of the cone. do not include the empty space for the pyramid. 7.. the side length of the square base of the pyramid is 8 units long. what is the base area of the pyramid? 8.what is the formula for the volume of a pyramid9. since the cone and the pyramid share the same vertex, what is the volume of the pyramid10.using the volume of the cone and the pyramid, find the volume of the composite shape. remember, the pyramid is empty. 11,. referring to the picture in number 1, what is the area of the composite base knowing that the square is empty? 12what is the formula to find the lateral surface area of a cone? (13find the lateral surface area of the cone14what is the lateral surface area shape of the pyramid? what is the formula for its area? 15to find the lateral surface area of the pyramid the length is still needed. calculate the lateral surface length of the pyramid. 16 now that the lateral surface length is known, what is the lateral surface area of the pyramid17. using the lateral surface areas of the cone and pyramid, along with the area of the composite base, what is the total surface area?