MTH 225-Introductory Statistics-Sample Test #2 Part I: Select the most perfect b

Question

MTH 225-Introductory Statistics-Sample Test #2 Part I: Select the most perfect best correct answer: 1 . In a group of 10 college students, 4 are business majors. You choose a 3 out of the l students at random. The distribution of the number of business majors you choose is (a) binomial with n-10 and p 0.4. (b) binomial with n 3 and p 0.4. (e) not binomial because the selections are dependent (d) not binomial because the selections are independent random variables Binomial distributions represent a- (a) discrete (b) continuous (c) none of the above. 2. random variables. Normal distributions represent a_ (a) discrete (b) continuous (c) none of the above. 3. - Part II: Mark each of the following sentences as True or False: 1· The margin of error for a 95% confidence interval for the mean increases as the sample increases.True/False) The margin of error for a confidence interval for the mean based on a specified sample size n, increases as the confidence level decreases. 2 When determining the sample size to estimate a population mean within a specified margin of error, the sample size required to obtain a confidence interval increases as the confidence level increases 3. (True/False) Part III: Complete all of the following questions AND show your work. Q#1 : A pizza shop owner wishes to find the 90% confidence interval of the true mean cost of a large plain pizza. A previous study showed that the standard deviation of the price was S0.46. How large should the sample be if she wishes to be accurate to within $0.10?

Explanation / Answer

Part (I).1. We choose 3 students, so n = 3 and probability of business major students, p = 4/10 = 0.4

So, the distribution is Bin (3, 0.4). Hence, Option (b) is the correct choice (Ans).

2. Binomial distribution represents a discrete random variable.

(Ans).

3. Normal distribution represents a continuous random

variable. (Ans).

Part(II)

1. Margin of error is inversely proportional to the sample size. So as the sample size increases, margin of error decreases.

Hence, the given statement is False. (Ans).

2. Margin of error increases with Confidence level. So the

given statement is False. (Ans).

3. For a fixed margin of error, as the confidence level

increases, sample size also increases. So, the given

statement is True. (Ans).

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