Statistics and Probability Answers

p=0.64

a=0.05

n=180

what is the point estimate of p?

what is the interval estimate of p?

The head of the PE Department of a certain high school claims that the mean height ofGrade 7 students is 163 cm. The mean height of 45 randomly selected Grade 7 studentsis 161 cm. Using 0.01 significance level, can it be concluded that the mean height ofGrade 7 students is different from 163 cm as claimed by the Head of the PE Department?

You are planning to buy a good quality cell phone in order to attend the online calss.The average price of 50 cellphones is ₱13,500 with a standard deviation of ₱573.65 and a confidence level of 99%. Find the corresponding confidence interval.

The Head of the Math Department announced that the mean score of

Grade 9 students in the first periodic examination in Mathematics was 89 and

the standard deviation was 12. 0ne student, who believed that the mean

score was less than this, randomly selected 25 students and computed their

mean score. She obtained a mean score of 85. At a 0.01 level of significance,

test the student's beliefs.

 You are taking a test to see if you have supernatural abilities that involves a deck of five cards that each show one of five symbols (which we will call (A, B, C, D, E)). The cards are placed in a sequence so that each card appears exactly once; no repeats are allowed. Your job is to guess the correct sequence. (a) How many different sequences are possible? (b) What is the probability that you guess all five cards in the sequence correctly? (c) What is the probability that the letters AB occur consecutively and in that order some where in the sequence?

 You are taking a test to see if you have supernatural abilities that involves a deck of five cards that each show one of five symbols (which we will call (A, B, C, D, E)). The cards are placed in a sequence so that each card appears exactly once; no repeats are allowed. Your job is to guess the correct sequence. (a) How many different sequences are possible? (b) What is the probability that you guess all five cards in the sequence correctly? (c) What is the probability that the letters AB occur consecutively and in that order some where in the sequence?

Each time you visit the state fair, you play some games at the Midway. One game has four prizes (A, B, C, D). (a) How many different four letter sequences are possible if each letter is chosen from {A, B, C, D} with repeats allowed? (b) How many different four letter sequences have each letter occurring exactly once? (c) How many different four letter sequences don't contain B? (d) How many different four letter sequences have two letters, each of which occurs twice?

Each time you visit the state fair, you play some games at the Midway. One game has four prizes (A, B, C, D). (a) How many different four letter sequences are possible if each letter is chosen from {A, B, C, D} with repeats allowed? (b) How many different four letter sequences have each letter occurring exactly once? (c) How many different four letter sequences don't contain B? (d) How many different four letter sequences have two letters, each of which occurs twice?

2. Consider all samples of size 2 from this population:

2 5 6 8 10 12

a. Compute the mean () and variance () of the population.

b. List all samples of size 2 and compute the mean for each sample.

c. Construct the sampling distribution of the sample means.

d. Calculate the mean of the () of the sampling distribution of the sample means.

e. Calculate the variance of the () of the sampling distribution of the sample means.

III – Find the approximate p-value given the following information:

1. A two-tailed test; computed t-value = 1.845; df = 10

2. A left-tailed test; computed t-value = 2.295; df = 21

3. A right-tailed test; computed t-value = 1.565; df = 27

4. A two-tailed test; computed t-value = 2.452; df = 12