Question

Problem #1. The American family has an average of two children. (a) What is the random variable? Describe in words. (b) You believe that the average is actually more than two. If you were conducting a hypothesis test what would the null and alternative hypotheses be? Make sure to use the correct language and notation. (c) Will you be conducting a left-tailed, right-tailed, or two-tailed test? Draw a general graph of your test. (d) State Type I and Type II errors in complete sentences. (e) State your sample size. Choose a number between 20 and 50. (f) Suppose your sample's mean is 2.1, and its standard deviations is 0.25. What distribution should you use to perform the hypothesis test? (If needed assume that the population is approximately normal.) (g) State your significance level αα. Choose between values 0.01, 0.05, and 0.1. (h) Conduct a hypothesis test and state your conclusion.

Answer 1

Answer: Here's my answer!

Step-by-step explanation:

(a) The random variable in this problem is the number of children in an American family.

(b) If conducting a hypothesis test, the null hypothesis (H0) would be that the average number of children in an American family is equal to two. The alternative hypothesis (Ha) would state that the average is actually more than two.

(c) Since the alternative hypothesis suggests that the average is more than two, the test would be a right-tailed test.

(d) Type I error: Rejecting the null hypothesis when it is actually true would be a Type I error. In this case, it would mean concluding that the average number of children in an American family is more than two when it is actually not.

Type II error: Failing to reject the null hypothesis when it is actually false would be a Type II error. In this case, it would mean failing to conclude that the average number of children in an American family is more than two when it actually is.

(e) The sample size is not provided in the question. Please provide a number between 20 and 50.

(f) Assuming the sample size is large enough and the population is approximately normal, the distribution to perform the hypothesis test would be the normal distribution.

(g) The significance level α (alpha) is not provided in the question. Please choose a value between 0.01, 0.05, and 0.1.

(h) Without the sample size and significance level, a hypothesis test cannot be conducted. Please provide the sample size and significance level to proceed with the hypothesis test and state the conclusion.