Statistics and Probability Answers

A manufacturer of paper box package claims that her manufacturing process is very accurate and that the mean length of a certain type of box 20m with a standard deviation of 0.1cm. You take a random sample of 29boxes and obtain a sample deviation of 0.15cm. Assume that the mean length of the boxes is normally disturbed. Test the null hypothesis that the true variance is 0.01 against the alternative hypothesis that the true variance is not equal to 0.01. Do you accept or reject her claim? Use 5% significance level.

A random sample of 10units of mobile phone batteries from manufacturer A gave a lifetime with standard deviation of 5 months while a random sample of 13 units of batteries from manufacturer B gave a lifetime with standard deviation of 4 months. Assume the population to be approximately normal with equal variances. Use a 0.10 level of significance.

How large a sample is needed if we wish to be 95% confident that the sample mean will be within 0.0005 of the true mean? Assuming the population standard deviation is 0.0015 and the population is normal.

A random sample of 10 mobile phone batteries has a lifetime with variance 16 months. Assuming the lifetime of batteries to be normally distributed, construct a 95% confidence interval for the variance of all such mobile phone batteries.

Five universities in Malaysia were surveyed. The sample contained 250 information technology students, 80 being women; 160 bioinformatics students, 40 being women. Compute a 90% confidence interval for the difference between the proportions of women in these two programs.

Firebrick Tire Company wants to increase sales of its long running, low end Roadmaster Tire brand with a new advertising campaign claiming they will last at least 28,000 miles [u=28,000 miles]. Tests with a random sample [n=30 tires] show a sample mean [x=$27,500 miles] with a sample standard deviation [s=1000 miles]. At a .05 level of significance, these tests indicate

a. Reject Ho: Z of -2.7386 less than -1.6450
b. Reject Ho: Z of -2.7386 less than 1.6450
c. Do not reject Ho: Z of 1.6450 less than 2.7386
d. Do not reject Ho: Z of -1.6450 less than 2.7386
e. None of the Above

In a random sample of 40 felons convicted of aggravated assault, it was determined that the
mean length of sentencing was 54 months, with a standard deviation of 8 months. Construct
and interpret a 95% confidence interval for the mean length of sentence for an aggravated
assault conviction.

From a population of 20,000 observations, a sample of 500 observations is selected. Calculate the standard error of sample mean if the population standard deviation equals 20

Ten individuals are chosen at random, from a normal population and their weights (in kg) are
found to be 63, 63, 66, 67, 68, 69, 70, 70, 71 and 71. In the light of this data set, test the claim
that the mean weight in population is 66 kg at 5% level of significance.

If X is a Poisson variate and p(X = 3) > p(X = 2) then find the minimum value of mean