Question

The governor of a state wanted to assess the public education system of the state. She instructed a group of researchers to create a test to assess the knowledge of every high school senior in the state. The researchers administered the tests and found that the average score was 34 points out of 100, with a standard deviation of 29 points. Complete paris (a) through (c) below. a. Identify the population and variable. Choose the correct population below. O A The population is the group of all high school teachers in the state. OB. The population is the group of all high school seniors in the state. OC. The population is the group of every state's governor. OD. The population is the group of all high school students in the state. Choose the correct variable below O A. The variable is the number of high school seniors. OB. The variable is the number of high school students O C. The variable is the test score. OD. The variable is the test length. b. For samples of size 150, find the mean and standard deviation of all possible sample mean test scores. Hi-(Type an integer or a decimal.) - (Round to one decimal place as needed.) c. Repeat part (b) for samples of size 300. H:-(Type an integer or a decimal.) q;= (Round to one decimal place as needed.)

Answer 1

Solution :

Given that ,

mean = $\mu$ = 84

standard deviation = $\sigma$ = 29

a) population = correct option is = B

variable = correct option is = C

b) n = 150

$\mu$_{$\bar x$} =  $\mu$ = 84

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 29 / $\sqrt$ 150 = 2.4

c) n = 300

$\mu$_{$\bar x$} =  $\mu$ = 84

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 29 / $\sqrt$ 300 = 1.8