1. A sample of 100 newborns has a normal distribution with an average of 5kg and the standard deviation of 0.5kg. The standard error is 0.05. A newborn named Richard is heavier than 84.13 percent of the newborns in the sample. Richard’s weight is_______

2. 3 kg

3. 45 kg

4. 55kg

5. 4kg

6. Not enough information.

2. Professor Pham surveys a random sample of 100 households in a community of 10,000 households. The average household income in this sample is $86,000. The sample standard deviation is $5000. The sampling distribution of the sample means has the mean of ___

3. $81,000

4. $85,500

5. $86,000

6. Not enough information

1. A company of 10,000 employees buys 100 raffle tickets for the company’s holiday party. The HR head checks the value of 16 random raffle tickets. She finds among the 16 raffle tickets that she checks, the average value is $22, and the standard deviation is $24. Assume that the sampling distribution of the sample means is normal and the population standard deviation equals sample standard deviation. The 95% confidence interval is ($16, $28).

   1. This confidence interval is not valid because N=16<100, so the central limit theorem does not apply.

   2. We are 95% confident that the average value of the 16 raffle tickets that the company buys is between $16 and $28.

   3. We are 95% confident that the average value of the 100 raffle tickets that the company buys is between $16 and $28.

   4. b&c.

   5. None of the above

2. ., z-obtained= 2.5, significance level . Assume that the sampling distribution is normal. We ____________

3. Reject the null hypothesis because if the null hypothesis is true, we would be more likely to obtain a sample mean further away from 12.

4. Reject the null hypothesis because if the null hypothesis is true, we would be more likely to obtain a sample mean closer to 12.

5. Reject the null hypothesis because5>0.05

6. Cannot decide because we do not know the sample mean.

Part II (75 points total): Short Answers

1. (10 points) The General Social Survey (GSS) has been administered to randomly selected samples of adults Americans since 1972 and explores a broad range of characteristics and issues, including confidence in the Supreme Court, attitudes about assisted suicide, number of siblings, and level of education. Please visit the GSS website for more information (https://gss.norc.org/).

The “GSS_2018.dta” data on Blackboard is the GSS data in 2018.

Variable “natrace” in GSS_2018 records the answer to the following question: “In your opinion, are we spending too much, too little, or about the right amount of money on improving the conditions of Blacks?” You can see part of the 2018 GSS questionnaire here: https://gss.norc.org/Documents/quex/GSS2018%20Ballot%201%20-%20English.pdf

Please summarize the opinions of the American adults in GSS_2018 on the amount of money the US is spending on improving the conditions of Blacks from the natrace variable. You can present your finding in the format of a table, a graph, or both. Please be sure to also explain your finding in words.

DETAILED ASSIGNMENT

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