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For a lottery to be successful, the public must have con dence in its fairness. One of the lotteries in Maryland is Pick-3 Lottery, where 3 random digits are drawn each day. A fair game depends on every value (0 to 9) being equally likely at each of the three positions. If not, then someone detecting a pattern could take advantage of that and beat the lottery. To investigate the randomness, we'll look at data collected over a recent 32-week period. Althought the winning numbers look like three digit numbers, in fact, each digit is a randomly drawn 1 numeral. We have 654 random digits in all. Are each of the digits from 0 to 9 equally likely? Here is a table of the frequencies.
Group Count %0 62 9.4801 55 8.4102 66 10.0923 64 9.7864 75 11.4685 57 8.7166 71 10.8567 74 11.3158 69 10.5509 61 9.327
(a) Set up the relevant null and alternative hypothesis.(b) Write down the test statistic to be used for testing the hypothesis.(c) What is the sampling distribution of the test statistic if the null hypothesis is true?(d) If the level of signi cance = 5%, write down the rejection region.(e) Based on the data, do you reject the null hypothesis? Justify.(f) Did you commit a type I error based on your conclusion to 2e above?
A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 47.2 , with a standard deviation of 10.2.
Sun Microsystems has approximately 50% of the high-end Unix machines market with its closest competitor being IBM. Suppose that 15 firms were in the market to purchase a high-end Unix machine. Assume that these firms listened to sales pitches by a..
Formulate the hypothesis that can be used to determine whether the sample data support the hypothesis that the mean fuel efficiency rating for midsize cars is greater than the mean fuel efficiency for large cars.
Use alpha level. 05 to compute and interpret Pearson's r and to test whether it is important (using all your steps for hypothesis test).
A study of the time spent shopping in a supermar- ket for a market basket of 20 specific items showed an approximately uniform distribution between 20 minutes and 40 minutes. What is the probability that the shopping time will be:
A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level
Distribution and the method of moments estimators of the parameters are alpha(hat)= 5.23 and lambda(hat) = 21.3. Find an asymptotic 95% confidence interval for alpha.
Suppose four heads appeared face up on four tosses of a coin. what is the probability that a head will appear face up in the next toss of the coin?
Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.
Researchers routinely choose an -level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower -level (e.g. 0.01)?
A concessionaire for the local ballpark has made a table of conditional values for the different alternatives also states of nature
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