1.5 HW Stats

Use the One Proportion applet to also report a theory-based p-value.

0.3962

Are the validity conditions met? Explain.

Yes, because the number of success (65) and failures (125) are each at least 10.

Are the validity conditions met? Explain. Multiple choice 2 Question 6

Yes, because the number of success (93) and failures (112) are each at least 10.

Give the value of the statistic.

p̂ = 0.342

b. Give the value of the statistic.

p̂ = 0.454

Use the One Proportion applet to also report a theory-based p-value.

0.0001

Use the One Proportion applet to report a simulation-based p-value. Choose the best among the following options

0.415

Which sample size, n, gives the smallest standard deviation of the null distribution where the long-run proportion, π, is 0.25?

60

Write out a conclusion in the context of the research question.

Based on the large p-value, we do not have strong evidence against the null hypothesis. We do not have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Tuesdays (compared to Thursdays or Saturdays) is greater than 0.333.

Write out a conclusion in the context of the research question.

Based on the small p-value, we have strong evidence against the null hypothesis. We have strong evidence that the long-run proportion of cardiac arrests among dialysis patients that happen on Mondays (compared to Wednesdays or Fridays) is greater than 0.333.

Patients with kidney disease often have a procedure called dialysis done to clean their blood if their kidneys can't do this properly. This procedure is often done three days per week, with Monday, Wednesday, and Friday often being those days. In terms of the dialysis treatments, these days are all the same except for the gap of two off days before the Monday treatment. Does this gap make a difference? Cardiac arrest and sudden death for patients undergoing dialysis for kidney disease are possibilities. In recent years, it has been noted that these types of patients have cardiac arrests on Mondays more often than what would be expected. A study published in Kidney International (Karnik et al., 2001) looked at 205 dialysis patients that had cardiac arrests on Monday, Wednesday, or Friday, the same days they had dialysis. They found that 93 of these happened on a Monday. Do we have convincing evidence of a larger pro

H0: π = 0.333 Ha: π > 0.333

Recall the previous exercise on cardiac arrests for kidney disease patients. Besides the Monday-Wednesday-Friday schedule for dialysis, many patients are on a Tuesday-Thursday-Saturday schedule. Again, like Monday, Tuesday is unique in that there is the same preceding two-day gap in dialysis. The researchers found that of the 190 cardiac arrests that took place for patients on the Tuesday-Thursday-Saturday schedule, 65 of them occurred on Tuesdays. Do we have convincing evidence of a larger probability of cardiac arrests occurring on Tuesdays compared to the other two days? Investigate by answering the following. a. Set up the correct null and alternative hypotheses in symbols.

H0: π = 0.333 Ha: π > 0.333

Suppose 10 coins are flipped, and the proportion of heads is recorded. This process is repeated many, many times to develop a distribution of these sample proportions. What is the predicted mean and standard deviation for this distribution of sample proportions?

Mean = 0.500, SD = 0.158

The theorem that states that if the sample size is large enough, the distribution of sample proportions will be bell-shaped (approximately normal), centered at the long run proportion π, with a standard deviation of is called:

The central limit theorem.

Suppose you are using theory-based techniques (e.g., a one-proportion z-test) to determine p-values. How will a two-sided p-value compare to a one-sided p-value (assuming the one-sided p-value is less than 0.50)? Question 2

The two-sided p-value will be exactly twice as large as the one-sided.

Use the One Proportion applet to report a simulation-based p-value. Choose the best among the following options Multiple choice 3 Question 6

Yes, because the number of success (93) and failures (112) are each at least 10.

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 30 free throws and she makes 18 (or 60%) of them. Are the validity conditions met for the one-proportion z-test? Question 3

Yes, because the number of success and failures are each at least 10.