The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 ("SOCR data 2008," 2013). Compute a 95% confidence interval for the mean economic dynamism of middle-income countries. Table #8.3.9: Economic Dynamism ($) of Middle Income Countries 25.8057 37.4511 51.915 43.6952 47.8506 43.7178 58.0767

Let X ~ U[0, 1] and Y ~ U[1,5] be two independent uniform random variables.

A researcher wants to study the effectiveness of three kinds of pain reliever. What do you suggest him? Two way ANOVA Test One way ANOVA Test Either O Both

From the list of convolutions below, select the statement that is incorrect. o (a) The sum of 2 i.i.d. Bern(p) RVs has a Bin(2, p) distribution. o (b) The sum of 5 i.i.d. Exp(3) RVs has an Erlang distribution with mean 5/3. o () The sum of 5 i.i.d. Pois(3) RVs has an Erlang distribution with mean 15. O (d) If Z, and Z2 are i.i.d. Nor(0,1), then Z + Z ~x(2). o (e) The sum of 100 i.i.d. Gamma(1, 1) RVs is approximately normal.

On average, 12 balls enters the room every minute. What is the probability that the 4th ball seconds to arrive and that at most 2 balls arrive between the 256th and 267th second? (Must ariables and give at least four decimal points)

On average, 12 balls enters the room every minute. What is the probability that the 3th ball takes up to 10 seconds to arrive and that at most 3 balls arrive between the 300th and 307th second? (Must use random variables and give at least four decimal points)

In a random sample of62professional actors, it was found that37were extroverts.

(a)Letprepresent the proportion of all actors who are extroverts.Find a point estimate forp. (Round your answer to four decimal places.)

(b)Find a 95% confidence interval forp. (Round your answers to two decimal places.)

lower limit

upper limit

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

(c)Do you think the conditionsnp>5 andnq>5 are satisfied in this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.