According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100:114 (46.7% girls). Suppose you don't believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 59 girls and 91 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7? Conduct a hypothesis test at the 5% level. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a) State the null hypothesis. H0: p ≥ 0.467 H0: p ≠ 0.467 H0: p ≤ 0.467 H0: p = 0.467

Part (b) State the alternative hypothesis. Ha: p > 0.467 Ha: p < 0.467 Ha: p = 0.467 Ha: p ≠ 0.467

Part (c) In words, state what your random variable P' represents. P' represents the percent of boys born in China. P' represents the number of girls born in China. P' represents the ratio of girls to boys in China. P' represents the percent of girls born in China. Part (d) State the distribution to use for the test. (Round your answers to four decimal places.) P' ~ ,

Part (e) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) ---Select--- =

Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If H0 is false, then there is a chance equal to the p-value that the sample ratio is 59 out of 150 or less OR 81 out of 150 or more. If H0 is false, then there is a chance equal to the p-value that the sample ratio is not 59 out of 150 or less OR 81 out of 150 or more. If H0 is true, then there is a chance equal to the p-value that the sample ratio is 59 out of 150 or less OR 81 out of 150 or more. If H0 is true, then there is a chance equal to the p-value that the sample ratio is not 59 out of 150 or less OR 81 out of 150 or more

. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot

Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α =

(ii) Decision: reject the null hypothesis do not reject the null hypothesis

(iii) Reason for decision: Since α > p-value, we reject the null hypothesis. Since α < p-value, we reject the null hypothesis. Since α > p-value, we do not reject the null hypothesis. Since α < p-value, we do not reject the null hypothesis.

(iv) Conclusion: There is sufficient evidence to conclude that the percent of girls born in China is not equal to 46.7%. There is not sufficient evidence to conclude that the percent of girls born in China is not equal to 46.7%

. Part (i) Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.) WebAssign Plot

Assume that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.. If 25 people are randomly selected, find the probability that their mean IQ score is less than 103. (a) .1587 (b) .8413 (c) 1.000 (d) .9938 23 Refer to question 19 above. If 100 people are randomly selected, find the probability that their mean IQ is greater than 103. (a) .8413 (b) 2.000 (c) .9772 (d) .0228 24 True or False. Because the total area under the normal standard distribution is equal to 1, there is a correspondence between area and probability. (a) True (b) False 25 True of False. A Z-score must be negative whenever it is located in the left half of the normal distribution. (a) True (b) False 26. The World Health Organization states that tobacco is the second leading cause of death in the world. Every year, a mean of 5 million people die of tobacco-related causes. Assume that the distribution is normal with µ = 5 (in millions) and ơ = 2 (in millions). Find the probability that more than 4 million people will die of tobacco-related causes in a particular year. (a) .3085 (b) .5000 (c) .6915 (d) -.5000 (e) .9772 27. Refer to question 26. What is the probability that the number of people who will die from tobacco-related deaths will fall between 3 million and 7 million in a particular year? (a) .1587 (b) .8413 (c) 1.000 (d) -1.000 (e) .6826 SHOW WORK

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Find the probability that the person has an IQ less than 110. Include a sketch of the graph and shade the area to be determined.

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person score would be grater than 140?

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15 What is the probability that a person would score between 85 and 115?

If you were the Minister of Health in Tanzania, and you had a budget of $100 million for all health activities, how much would you spend on malaria, and how would you spend it.

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.  Given a class with 12 students, what is the probability that the class' average IQ score is less than 115?

In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.5 mm.

Find a 95% lower confidence bound for the mean wall thickness. (Round the final answer to three decimal places.)

The 95% lower confidence bound is

Consider an MPT that is backed by 100 mortgages with average balance of $350,000 and monthly payment. The MPT has a WAC = 5% and WAM = 60 months. There is no servicing fee on this security. Assuming the prepayment model of CPR=5% and market rate is 3%, how much should this security sell for?