C) Develop a hypothesis test for H0 : theta = theta₀ versus Ha : theta= theta₀, where theta₀ is a constant, at the alpha significance

level.

Q2. Burger restaurant prots This question may be handwritten and then scanned to pdf, or typed up. The three most popular menu items of a local burger restaurant are beef burger, chicken burger, and sh burger. Let W, X, and Y denotes the weekly sales of beef, chicken, and sh burgers, respectively. Suppose the random variables W, X, and Y are independent and normally distributed with means #1, p2, and p3 and variances 02, 102, and bo2, respectively, where a and b are known constants. The prot for a beef burger is $2, a chicken burger is $1, and a sh burger is $0.40. Hence, the expected weekly prot from these three menu items is 6 : 2W + X + 0.4Y. (a) Find EM] and var(6). State the distribution Of 6. [4 marks] (b) The owner has made independent observations of W, X, Y for the past n weeks. Let W, X, and 37 denote the sample means, and 33V, 3%, and S32; their respective sample variance. Let 63:2W+X+0.4}7 and S(SEV+ES+%S). U, A 66 i4+ +0 16b N 1530\"\" a . 510 H Show that T