Assisted Reproductive Technology (ART) is a collection of techniques that help f

Question

Assisted Reproductive Technology (ART) is a collection of techniques that help facilitate pregnancy (e.g. in vitro fertilization). A 2008 report by the Centers for Disease Control and Prevention estimated that ART has been successful in leading to a live birth in 31% of cases. A new fertility clinic claims that their success rate is higher than average. A random sample of 30 of their patients yielded a success rate of 40%. A consumer watchdog group would like to determine if this provides strong evidence to support the company's claim.

1. Chose the hypotheses to test if the success rate for ART at this clinic is significantly higher than the success rate reported by the CDC. Choose the hypotheses to test if the success rate for ART at this clinic is significantly higher than the success rate reported b the CDC.

A. H0H0: The success rate for ART at this clinic is the same as the rate reported by the CDC.  
HAHA: The success rate for ART at this clinic is higher than the rate reported by the CDC.
B. H0H0: The success rate for ART at this clinic is higher than the rate reported by the CDC.
HAHA: The success rate for ART at this clinic is the same as the rate reported by the CDC.
C. H0H0: The success rate for ART at this clinic is higher than the rate reported by the CDC.
HAHA: The success rate for ART at this clinic is lower than the rate reported by the CDC.
D. H0H0: The success rate for ART at this clinic is lower than the rate reported by the CDC.
HAHA: The success rate for ART at this clinic is the same as the rate reported by the CDC.

2. To setup a simulation for this situation, we let each patient be represented with a card. We take 100 cards, black cards represent successful ART cycles and red cards represent unsuccessful ART cycles. Shuffle the cards and draw with or without replacement cards representing the random sample of patients. Calculate the proportion of black or red cards in the sample or deck and call it ps. Repeat 10,000 times and plot the resulting sample proportions. The p-value will be the proportion of simulations where ps greater than or less than or beyond) ( ) .

3.Below is a histogram showing the distribution of psps in 10,000 simulations under the null hypothesis. Estimate the p-value using the plot and use it to evaluate the hypotheses.

A. The p-value is substantially smaller than 0.05 and we should reject the null hypothesis.
B. The p-value is substantially larger than 0.05 and we should reject the null hypothesis.
C. The p-value is substantially larger than 0.05 and we should not reject the null hypothesis
D. The p-value is substantially smaller than 0.05 and we should not reject the null hypothesis.

Explanation / Answer

Question 1

Here hypothesis are

A. H0 The success rate for ART at this clinic is the same as the rate reported by the CDC.  
HA: The success rate for ART at this clinic is higher than the rate reported by the CDC.

Option A is correct.

Question 2

To setup a simulation for this situation, we let each patient be represented with a card. We take 100 cards, 31 black cards represent successful ART cycles and 69 red cards represent unsuccessful ART cycles. Shuffle the cards and draw with replacement 30 cards representing the random sample of patients. Calculate the proportion of black cards in the sample and call it ps. Repeat 10,000 times and plot the resulting sample proportions. The p-value will be the proportion of simulations where ps is greater than 0.31 .

(3)

Here p - value = 0.11 + 0.07 + 0.03 + 0.02 + 0.01 + 0.005 = 0.245

Here the p - value is substantially larger than 0.05 and we should not reject the null hypothesis.

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