Problem 1; #11.1: If is a value of a random variable having an exponential distribution, find k so that the interval from 0 to kx is a (1 -a)100% confidence interval for the parameter 0.
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A: Given that Sample size n =900 Favorable cases x =504 Sample proportion p^=x/n =504/900 =0.56
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesisQuestion 1 The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College Question 1 options: must be more than 22, since the population is always larger than the sample is 22 since the sample mean is an unbiased estimator of the population mean could be larger, smaller, or equal to 22 must be less than 22, since the sample is only a part of the population
- question 27 59% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 124 of the 243 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.05? The null and alternative hypotheses would be: Ho: p= (please enter a decimal) H1: p< (Please enter a decimal) 2.The test statistic _______ (please show your answer to 3 decimal places.) 3.The p-value = ______ (Please show your answer to 4 decimal places.)Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hoursQuestion 16: According to a University Center for Logistics Management, 4% of all merchandise sold in the United States gets returned. A Seattle department store sampled 89 items sold in January and found that 5 of the items were returned.If you have the following null and alternative hypotheses for a test you are running:H0:p=0.04H0:p=0.04Ha:p≠0.04Ha:p≠0.04Calculate the test statistic, rounded to 3 decimal places z=
- QUESTION 9 The Department of Trade and Industry (DTI) conducted a survey to estimate the average number of employees per small and medium-sized enterprises (SME) in Free State. For a random sample of 144 SMEs in Free State, the DTI found that the average number of employees was 24.4. Assume that the population standard deviation is 10.8 employees and that the number of employees per SME is normally distributed. Using this information and rounding off the z or t values that you derive to 2 decimal places, the 95% confidence interval of the average number of employees per SME in Free State is for the lower limit andfor the upper limit. (Note: write your final answers to 3 decimal places and when writing your answer use "." (3.250) instead of "," (3,250) with no spaces between digits).QUESTION 11 An educator estimates that the dropout rate for seniors at high schools in Colorado is 15%. Last year in a random sample of 300 Colorado seniors, 34 withdrew from school. At α = 0.10 level of significance, is there enough evidence to reject the educator’s claim? Yes, because the p-value is 0.075 Yes, because the z-statistic is 1.6 No, because the p-value is 0.038 Yes, because the p-value is larger than 0.15Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will be y − L. The chance of a safe return is 50%. Now suppose that there are two identical merchants, A and B, who are both risk averse expected utility maximisers with utility of income given by u(y) = ln y. The income of each merchant will be 8 if their own ship returns and 2 if it sinks. As previously, the probability of a safe return is 50% for each ship. However, with probability p ≤ 1/2 both ships will return safely. With the same probability p both will sink. Finally, with the remaining probability, only one ship will return safely. (iv) Compute the increase in the utility of each merchant that they could achieve from pooling their incomes (as a function of p). How does the benefit of pooling depend on the probability p? Explain intuitively why this…
- Question 16 Match the p-values with the appropriate conclusion: I. 0.00001 II. 0.0297 III. 0.0721 IV. 0.4490(a) The evidence against the null hypothesis is significant, but only at the 10% level. (b) The evidence against the null and in favor of the alternative is very strong. (c) There is not enough evidence to reject the null hypothesis, even at the 10% level. (d) The result is significant at a 5% level but not at a 1% level.QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis?see pictures (question 1-3) 1) 2 answer and choose one (right-tailed, left-tailed, two-tailed) 2) critical value 3) t=