An investment website can tell what devices are used to access the site. The sit

Question

An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via "smart phones," so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes). They draw a random sample of 300 investors from their customers. Suppose that the true proportion of smart phone users is 35%. Complete parts a through c below. a) What would you expect the shape of the sampling distribution for the sample proportion to be? Normal Uniform Exponential None of these b) What would be the mean of this sampling distribution? The mean would be. (Type an integer or a decimal.) The mean cannot be determined. c) If the sample size were increased to 600, would your answers change? Explain. No, the shape and symmetry characteristics would still be approximately the same and the mean would still be the same. No, the shape, symmetry characteristics, and mean will only change if the sample size is increased by at least 1000. Yes, although the mean would still be the same, the shape and symmetry characteristics would change. Yes, although the shape and symmetry characteristics would remain, the mean would increase.

Explanation / Answer

a) Nomal distribution

        since n = 300, p = 0.35, np = 300*0.35 = 105        and         nq = 300*0.65=195

      Here np and nq values are greater than 5. Therefore, the given binomal data follows nomal distribution.

b) Answer: 0.35

Mean of the sampling distribution = np =300*0.35 = 105

c) Correct Answer: Option (D)

Since np = 600*0.35 = 210, Therefore, Mean is increased when n is increase

but the shape and symmetry characteristics would be remain. since n = 600, p = 0.35, np = 600*0.35 = 210        and         nq = 600*0.65=390

      Here np and nq values are greater than 5. Therefore, the given binomal data follows nomal distribution.

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