The lowest significance level at which the null hypothesis can be rejected is called the:
Answer(s): C
The lowest significance level at which the null hypothesis can be rejected is called the p-value of the test. Thus, if the p-value is less than the significance level, the null hypothesis can be rejected at that significance level.
The sponsors of a well-known charity came up with a unique idea to attract wealthy patrons to the $500 a plate dinner. After the dinner, it was announced that each patron attending could buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50-50. If you bought a set of 20 tickets, what is the chance that you will win 15 or more prizes?
Answer(s): A
This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(p^r)[q^(n-r)]/r!(n-r)!.Here n = 20, p = 0.5 and q = 0.5 and r = 15,16,17,18,19,20. Therefore we have P(15) = 20!(0.5^15)(0.5^5)/15!5! = 0.0148P(16) = 20!(0.5^16)(0.5^4)/16!4! = 0.0046P(17) = 20!(0.5^17)(0.5^3)/17!3! = 0.0011P(18) = 20!(0.5^18)(0.5^2)/18!2! = 0.0002P(19) = 20!(0.5^19)(0.5^1)/19!1! = 0.00002P(20) = 20!(0.5^20)(0.5^0)/20!0! = 0.000001The sum adds up to 0.207.
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one hour period twenty-five customers buy gasoline at this station.What is the probability that more than ten and less than fifteen customers pay in cash?
Answer(s): E
Binomial distribution: n!(p^r)(q^(n-r))/r!(n-r)!. n = 25, r = 10, p = 0.4 q = 0.6 P(11) = 25!(0.4^11)(0.6^14)/11!14! = 0.1465P(12) = 25!(0.4^12)(0.6^13)/12!13! = 0.1140P(13) = 25!(0.4^13)(0.6^12)/13!12! = 0.0760P(14) = 25!(0.4^14)(0.6^11)/14!11! = 0.0434Summing up: 0.3799.
What monthly payment, beginning next month, would pay off a debt of $1,000 over 15 months, if the interest rate on the debt is 18% per year, compounded monthly?
On the BAII Plus, press 15 N, 18 divide 12 = I/Y, 1000 PV, 0 FV, CPT PMT. On the HP12C, press 15 N, 18 ENTER 12 divide i, 1000 PV, 0 FV, PMT. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.
Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?
Answer(s): B
Interval estimate can be found from p +/- z[p(1-p)/n]^0.5. Here we have n = 2000, p = 1600/2000 = 0.8 and z = 1.96 (for 95%).Therefore 0.8 +/- 1.96*0.008944 and we get 0.7825 and 0.8175.
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