Math Answers

How many possible random samples of size 4 can be drawn from a population of size 8?

1. For a sample of 35 items from a population for which the standard deviation is σ= 20.5 , the sample mean is 458.0. At the 0.05 level of significance, test H₀: μ= 450  versus H₁: μ> 450  . Determine and interpret the p-value for the test.

1. At a certain college, new students are weighed when they join the college, new students are weighed when they join the college. The distribution of weights of students at the college when they enroll has a standard deviation of 7.5 kg and a mean of 70kg. A random sample of 90 students from the new entry were weighed and their mean weight was 71.6kg. Assume that the standard deviation has not changed. Test at 5% level, whether there is evidence that the mean of the new entry is more than 70kg.

Perform your hypothesis testing under the 5 steps used when performing a hypothesis test. State your conclusion clearly.

1. Suppose our p-value is .044. What will our conclusion be at alpha levels of .10, .05, and .01? 

1.     Suppose we are interested in finding a 99% confidence interval for the mean overall score of students at a certain school. Five students are sampled, and their overall scores are 560, 500, 470, 660, and 640.

a.      What is the standard error of the sample mean?

b.      Find a 90% confidence interval for the mean test score.

1.     i.  What happens to the margin of error when sample size increases? Does it increase, decrease, or stay the same?

ii.    How does this affect the size of the resulting confidence interval?

1.  i. Compare  Z distribution and Normal Distributions.

ii. What are the properties of the t distribution?

iii. Find the values for each.

a. t _𝛼/2 and n = 15 for the 98% confidence interval for the mean

    b. t _𝛼/2 and n = 10 for the 90% confidence interval for the mean  

Three balls are drawn in succesion without replacement from a box of 2 red balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R. Complete the table below

Evaluate this integral x(x²+4)dx / x⁴+9

Find the mean of the probability distribution of the random variable X which can take only values 2,4,5, and 9, given that P(2)=9/20, P(4)=1/20, P(5)=⅕, P(9)=3/10