Statistics and Probability Answers

Find the null and alternative hypothesis of the following:

1. 25 brand A cigarettes had an average nicotine content of 5mg, while 40 brand B cigarettes had an average nicotine content of 4.8mg. If the standard deviation of nicotine content if 1.6mg, does brand B have a lesser nicotine content with a 96% confidence level?
2. Fifteen pupils from an international school have a mean of 110 and a variance of 64 while 20 pupils from an integrated school have a mean IQ of 114 and a variance of 78. Is there a significant difference between their mean IQs using a 0.02 level of significance?

For the given probability distribution function

X=x 1. 2 3. 4. 5

P[X=x] 0.1 0.3 0.2 0.2 0.2

E(x) =?

E(2x+5) =?

E(x/2+3)=?

E(x ² )

For the set of data below, determine the 5 number summaries. Construct the resulting box and whisker plot. (20 pts) 5, 3, 8, 6, 1, -10, 3, 9, 7, 4, 2, 

1.   The mean annual wage of male workers in a particular company was Ksh. 67952 and that of female workers was Ksh. 61295 each year. The standard deviation for the two samples is Ksh. 3202 and Kshs.3758, respectively. Assuming the measurements are from random samples of 24 males and 27 females we want to investigate whether the mean salary of males is higher than that of females at α=0.05. Find:

a.      The test statistic

b.     Remember that the Null hypothesis will be rejected if ... (Give the missing value).

The mean annual wage of male workers in a particular company was Ksh. 67952 and that of female workers was Ksh. 61295 each year. The standard deviation for the two samples is Ksh. 3202 and Kshs.3758, respectively. Assuming the measurements are from random samples of 24 males and 27 we want to investigate whether the mean salary of males is higher than that of females at α=0.05.

The weights (in pounds) of preschool children are 41, 34, 43, 29, 35, 39, 47, 20, 21, 33, 32, 25, 44, 30, 22 ...find the 25th and 60th percentile for these weights

Petroleum pollution in ocean stimulates the growth of certain bacteria. An assessment of this group has been made by counting the bacteria in each of the five randomly chosen specimens of ocean water (of a fixed size). The count obtain were as follows 65, 43, 46, 62, 54 find the standard deviation of a sample of numbers round answer to two decimal places.

The workers union at a particular university is quite strong. About 94% of all workers employed by the University belong to the workers union. Recently, the workers went on strike, and now a local TV station plans to interview 5 workers (chosen at random) at the University to get their opinions on the street. What is the probability that exactly 4 of the workers interview our union members? Round your response to at least three decimal places.

The manufacture of fertilizer guarantees that, with the aid of the fertilizer, 75% of planted seeds will germinate. Suppose the manufacturer is correct. If 7 seeds planted with the fertilizer are randomly selected, what is the probability that more than 5 of them germinate? Carry your intermediate computations to the least four decimal places, and round your answer to two decimal places.

1. An X-bar control chart monitors the mean of a process by checking that the average stays between and . When the process is under control,

(a) What is the probability that five consecutive sample means of n cases stay within these limits?

(b) What is the probability that all of the means for 100 days falls within the control limits?