MULTIPLE CHOICE Choose the one alternative that best commpletes the statement or

Question

MULTIPLE CHOICE Choose the one alternative that best commpletes the statement or anawers the q 6) A relative frequency histogram for the sale prices of homes sold in one city during, 2010 is shown6) below. Based on the histogram, is a large sample necessary to conduct a hypothesis test about the mean sale price? f so why? Frequency 0 20 010 01013 20 25 30 35 43 Sale price of home 00 A) Yes; data do not appear to be normally distributed but bimodal C) No; data appear to be normally distributed. D) Yes; data do not appear to be normally distributed but skewed left. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. sample of 160 students, 18 were found to be overweight. At a-0.05, test the daim. 18) A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is 17) A recent study claimed that at least 15% ofjunior high students are overweight. In a 17) less than 36,000 miles. To check the claim, the firm randomly selects and tests 18 of these -0.05, test the shipping firm's claim. Round the lest statistic to the nearest thousandth. 19) Use a t-test to test the claim ·21 ata-001, given the sample statistics n-12,--222, 15) tires and gets a mean lifetime of 35,350 miles with a standard deviation of 1200 miles. At a 19) and s 2.2 Round the test statistic to the nearest thousandth. 20) In order to set rates, an insurance company is trying to estimate the number of sick days take per year. Based on earlier studies, they will 2) that full time workers at a local bank assumed that s - 2.1 days. a) How large a sample must be se be 95% confident that their estimate is within i day of the true mean? b) Repeat part (a) using a 98% confidence interval, which level of confidence requires a larger sample size? Explain. if the company wants to

Explanation / Answer

Q16

The given histogram is not symmetric, it is right skewed. Hence, it cannot be a Normal Distribution. Consequently, a larger sample size would be required so that Central Limit Theorem can be applied. Thus,

Answer option B ANSWER

Q17

Let X = number of junior high students who are overweight in a sample of 160 students. Then, X ~ B(160, p), where p = probability of a junior high student being overweight.

Claim :

At least 15% of junior high students are overweight.

Hypotheses:

Null H0 : p = p0 = 0.15   Vs HA : p < 0.15

Test Statistic:

Z = (p0 - pcap)/{ p0(1 - p0)/n} where

pcap = sample proportion = 18/160 = 0.1125and

n = sample size = 160.

Calculations:

Z = (0.15 - 0.1125)/{ (0.15 x 0.85)/160}

   = (0.0375)/0.000796875

   = 0.0375/0.0282

   = 1.328

Distribution, Critical Value and p-value:

Under H0, distribution of Z can be approximated by Standard Normal Distribution, provided

np0 and np0(1 - p0) are both greater than 10.

So, given a level of significance of %, Critical Value = upper % of N(0, 1), and

p-value = P(Z > Zcal)

Using Excel Functions of N(0, 1) for = 5%, Critical Value = 1.645 and

p-value = P(Z > 1.328) = 0.0921.

Decision Criterion (Rejection Region):

Reject H0, if Zcal > Zcrit or if p-value < .

Decision:

Since Zcal < Zcrit, p-value > , H0 is accepted.

Conclusion :

There is not enough evidence to suggest that the claim is valid.

DONE

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