1. A random sample of n = 20 products are taken from the production lines of a factory. Let = 1,..., 20, IID Xi Bernoulli(p) be the indicator of whether the i-th product defective for i where Р denotes the proportion of defective products in the population. It is desirable to test whether the the proportion of defective products is below 30%. (a) State the null hypothesis Ho and the alternative hypothesis Ha. (b) Describe the events of Type I error and Type II error in the procedure of making statistical decisions. 20 (c) Let T i=1 ₁X₁ denote the number of defective items in the sample. Suppose that we decide to reject Hỏ if T ≤ 4. Let π(p) denote the corresponding power function, i.e., π(p) = Pr (T ≤ 4|p). Determine the value of (p) at the points p = 0, 0.1, 0.2, 0.3,..., 0.9, and 1.0 and sketch the power function. (Hint: Use the statistical table for Binomial distribution.) = (d) What is the size of the test procedure in part (c), i.e., the maximum probability of making Type I error? (e) What is the power of the test procedure in part (c) when p = 0.1? (Hint: Both part (d) and part (e) can be obtained immediately from the power function (p).)

A: The original problem is related to a die is rolled two times.

A:

A: Given the data of a survey of 15 teachers who were asked how many paintings they have in their…

A:

A: The normal distribution is the continuous probability distribution and has parameters mean and…

A:

A:

A: From part e:For model 1; 95% CI and PI are: (168.5648, 175.9918) and (163.7609, 180.7957)For model…

A: This is a problem of differentiation. Based on the general formual we will answer the question.

A: (a) Given that the percentage of stadiums have just built in the past 20 years is, P=15%=15/100=0.15…

A:

A:

A:

A:

A:

A: 8r-rs.........A given r=6 s=5  put r and s value in A

A: The scatter plot drawn using the data is displayed below.     Thus, the correct option is,…

A:

A:

A: solve the integration by part

A:

A:

A: Given information- Population mean, μ = 8 minutes Sample size, n = 14 Sample mean, x-bar = 9.1…

A: Hello thank you for the question, As you have mentioned question number b & c, answering only…