Statistics and Probability Answers

APPLICATION:

an experimental study was conducted by a researcher to

determine if a new time slot has an effect on the performance

of pupils in mathematics. Fifteen randomly selected learners

participated in the study. Toward the end of the investigation, a

standardized assessment was conducted. The sample mean x̄= 75 and s=5. In standardization of the test, the mean was

65 and standard deviation was 8. Based on the evidence at

hand, is the new time slot effective? Use α = 0.05.

In a certain food stall, 278 out of 500 randomly selected consumers to indicate their preference for a new kind of food combination. Use a 99% confidence interval to estimate the true proportion ρ who like the new food combination.

Test the hypotheses, given p=0.42, p is not equal to 0.42, sample size=150, sample proportion=0.45, alpha =0.05

If a random sample of 38 public elementary schools is selected, what is the probability that the number of students enrolled is 452

an agronomist believes that a newly developed fertilizer will increase the mean harvest of eggplants by more than 2.5 kg. twenty six plants are treated with fertilizer and have a mean of 10.5 kg with standard deviation of 1.2. it is known that the population mean was 7.5 kg. test the claim at 0.01 level of significance  

Answer in (Permutation and Combination)

1. A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 4 science courses, any of 3 humanities courses, and any of 2 mathematics courses, how many ways can she arrange her program?
2. A clothing store wants to stock sweatshirts that come in four sizes (small, medium, large, x-large) and in three colors (yellow, blue, and white). How many different types of sweatshirts will the store have to stock?
3. For her birthday, Karla received a new wardrobe consisting of 5 shirts, 3 pairs of pants, 2 skirts, and 3 pairs of shoes for her birthday. How many new outfits can she make?

1.   A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 4 science courses, any of 3 humanities courses, and any of 2 mathematics courses, how many ways can she arrange her program?

2.   A clothing store wants to stock sweatshirts that come in four sizes (small, medium, large, x-large) and in three colors (yellow, blue, and white). How many different types of sweatshirts will the store have to stock?

3.   For her birthday, Karla received a new wardrobe consisting of 5 shirts, 3 pairs of pants, 2 skirts, and 3 pairs of shoes for her birthday. How many new outfits can she make?

A hog raiser in a certain province uses two methods of pig-farming: intensive pig farming, where pigs are housed indoors in group-housing or straw-lined sheds; and extensive pig farming, where pigs are allowed to wander around the farm or fence. Test the hypothesis whether or not the mean weight of pigs in intensive farming is better than the extensive farming based from the mean weight of the pigs in the sample with data shown below. Use a one-tailed test at 𝛼 = 1%. Determine the Zcritical value of the problem above.

Solve for the t-computed value of the following. Write your answer to the nearest

hundredths. Show the complete solution.

1. "\\chi" =15 "\\mu" = 12 s = 4 n = 12
2. "\\chi" = 7.8 "\\mu" = 10 s = 5.1 n = 10
3. "\\chi" = 5 "\\mu" = 5.3 s = 0.14 n = 8
4. "\\chi" = 7.2 "\\mu" = 9.1 s = 1.8 n = 15
5. "\\chi" = 5 "\\mu" = 7 s = 3 n = 10

Given 𝜇 = 45, and 𝜎 = 5.5. (7 points)

a. What is the raw score when 𝑧 = −1.57?

b. What is the raw score when 𝑧 = 2.09?

c. What is the raw score when −0.48 < 𝑧 < 1.4?

d. What is the raw score when −2.17 < 𝑧 < 1.79? e. What is the raw score when 𝑧 = 0.09?