Statistics and Probability Answers

Professor Coffey is studying a population of the elementary school pupils in a school district with data on all its children. Dr Meyer suggests she calculate a confidence interval to estimate the mean age these children. Professor Coffey responds that it is not necessary. Why.

100 people are asked to choose a name for a baby. They are given 14 names to choose from. What is the probability 2/3 of the 100 people will choose the same name?

The manager of a restaurant in Malacca claims that waiters working in all restaurants in Malacca earn an
average of RM150 or more in tips per week. A random sample of 25 waiters selected from restaurants of
Malacca yielded a mean of RM139 in tips per week with a standard deviation of RM28. Assume that the
weekly tips for all waiters in Malacca have a normal distribution. Using 1% significance level, can you
conclude that the manager’s claim is true?

A food company is planning to market a new type of frozen yogurt. However, before marketing this
yogurt, the company wants to find what percentage of the people like it. The company’s management
has decided that it will market this yogurt only if at least 35% of the people like it. The company’s
research department selected a random sample of 400 persons and asked them to taste this yogurt. Of
these 400 persons, 112 said they like it. Test at 2.5% significance level, can you conclude that the
company should market this yogurt? (5 marks)

the values below are the scores (maximum 20) obtained in an aptitude test by a random sample of 11 graduates. it is known that for the non-graduate population the median score is 12. is there evidence, at the 10% significance level, that graduate achieve a higher median score than the non-graduate population?
14 15 09 10 10 13 14 19 12 16 13

Lauren has a standard deck of playing cards, which contains 52 cards. If she randomly draws a card from the deck, what is the probability of drawing a red face card?

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

The U.S Bureau of the census reported mean hourly earnings in the wholesale trade industry of u=9.70 per hour in 1987. A random sample of n=49 wholesale trade workers in a particular city showed a sample mean hourly wage of x=9.30 per hour with a standard deviation of s=1.05 per hour. Test to see if wage rates in the city differ significantly from the reported 9.70. Test to see if wage rates in the city differ significantly from the reported $9.70. Use Alpha=.05.

a. Reject Ho: Z of 2.6667 greater than 1.960
b. Reject Ho: Z of 2.667 greater than 1.645
c. Reject Ho: Z of -2.6667 less than -1.960
d. Do not reject Ho: Z of .3810 less than 1.960
e. None of the above
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Company A is a microcomputer producer. The following data represents Company A’s yearly sales volume and its advertising expenditures over a period of 8 years. Sales in millions of dollars and advertising is in $10,000.

1993 15 32
1994 16 33
1995 18 35
1996 17 34
1997 16 36
1998 16 36
1999 19 39
2000 24 42

Using the method of least squares, what is the estimated regression line between sales and adverting, and the predicted sales in dollars, whth an advertising expenditure of $400K actual dollars as scaled to 40.

a. Sales=-10.4211 =.7895 Advertising: Sales $315,790
b. Advertising= 16.7143 + 1.0714 Sales: Sales $59.57 Million
c. Sales=.7895 + 10.421 Advertising: Sales $416.63 Million
d. Sales= -10.4211 + .7895 Advertising: Sales= $21.16 Million
e. None of the Above

The heights of a group of 1000 people are measured, and found to be distributed
normally with a mean height of 178 cm and a standard deviation
of 12 cm.
(a) How many people do we expect to find with a height of 178 cm or
less?
(b) How many people do we expect to find with a height between 166 cm
and 190 cm?