Statistics and Probability Answers

A. Find the length of the confidence interval (s = standard deviation)

1. s = 3

n = 250

Confidence level = 95%

2. s = 6

n = 400

Confidence level = 99%

B. Determine the sample size, given the following data.

1. s = 5

E = 2.42

Confidence level = 95%

2. You want to estimate the mean gasoline price within your town to the margin of error of 6 centavos. Local newspaper reports the standard deviation for gas price in the area is 30 centavos. What sample size is needed to estimate the mean gas prices at 99% confidence level?

3. Carlos wants to replicate a study where the highest observed value is 14.8 while the lowest is 14.2. He wants to estimate the population mean µ to the margin of error of 0.025 of its true value. Using 95% confidence level, find the sample size n that he need.

A consumer advocacy group suspects that a local supermarket’s 500 grams of sugar actually weigh less than 50 grams. The group look a random sample of 20 such packages, weigh each one, and found the mean weight for the sample to be 496 grams with standard deviation of 8 grams. Using 1% significance level, would you conclude that the mean weight is less than 500 grams? Also, find the 99% confidence interval of the true mean.

It was found that 90% of cucumber seeds sown in the soil germinate. Determine the most likely

number of germinated grains if there are 70 grains in the package.

The following sample of nine measurements was randomly selected from a normally distributed population:11,10,8,7,14,9,10,12

Test for significant difference between the sample mean and the population mean 10.Use a=0.05.

The joint PDF of the random variables f(x,y)=8xy,0<x<1, 0<y<x

f(x,y)=8xy,0<x<1, 0<y<x. Find the marginal probability density function of Y.

A certain population has a variance of 2.5, and a sample size of 4 is used to obtain the sampling distribution of the sample mean of this population. What is the variance of the sampling distribution of the sample mean?

Write your answer as a fraction in lowest terms.

Determine the given and compute the test statistic of the problem below using Central Limit Theorem, and construct the rejection region for each.

A certain group of welfare recipients receives relief goods with a mean amount of Php 500 per week. A random sample of 75 recipients is surveyed and found that the mean amount of relief goods they received in a week is Php 600 and a standard deviation of Php50.00 . Test the claim at 1% level of significance is not Php 500 per week and assume that the population is approximately normally distributed.

Determine the given, formulate the null and alternative hypothesis in words and in

symbols, and the appropriate test statistic.

A company produced ethyl alcohol and claimed to have a mean alcohol content of 70%. A random sample of 80 of ethyl alcohol was take as sample to verify this claim. It was found out that the mean alcohol content is 65% with a standard deviation of 2%. Test the claim at 5% level of significance and assume that the population is normally distributed.

Determine the given, formulate the null and alternative hypothesis in words and in

symbols, and the appropriate test statistic.

A seller claimed that her lip tint has a mean organic content of 90%. A rival seller asked 60 users of that lip tint and found that it has a mean organic content of 85% with a standard deviation of 5%. Test the claim at 1% level of significance and assume that the population is approximately normally distributed.