The senior class president of a large university claimed that 55% of the senior class was interested in going on the senior trip. To test this claim, the senior class president conducted a survey of a random sample of 80 seniors and 42 said that they wanted to go on the senior trip. To better understand the significance of the survey results, a simulation was devised based on the claim that 55% of the seniors wanted to go on the trip, each of sample size 80, simulated 200 times. Explain how the results of the simulation can be used to support or refute the senior class president's claim.
Proportion of Students Interested in the Trip
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
(Note: don't use percents as a sample proportion.)
Since the simulation shows [ ] with a sample proportion of [ ] or [ ], the claim that 55% of the senior class wants to go on the senior trip is [ ].
Since the simulation shows a range of sample proportions for each proportion of students interested in the trip, we can use it to determine how likely it is that a sample proportion of 42/80 (0.525) or higher would be obtained if the true proportion of students interested in the trip was actually 55%. If the proportion of 0.525 falls within the range of proportions obtained from the simulation, then we can consider the result consistent with the claim that 55% of the senior class wants to go on the senior trip. However, if the proportion of 0.525 falls outside of the range of proportions obtained from the simulation, then we have evidence to refute the claim.
Therefore, the results of the simulation can be used to support or refute the senior class president's claim depending on whether the sample proportion of 0.525 falls within or outside the range of sample proportions obtained from the simulation. The simulation result will provide us with a level of significance to determine whether or not to reject the null hypothesis.
Bella rolled a die 100 times and 18 of the 100 rolls came up as a six. She wanted to see how likely a result of 18 sixes in 100 rolls would be with a fair die, so Bella used a computer simulation to see the proportion of sixes in 100 rolls, repeated 100 times. Based on the results of the simulation, what inference can Bella make regarding the fairness of the die?
Proportion of Sixes Rolled
0.05
0.1
0.15
0.2
0.25
0.3
(Note: don't use percents as a sample proportion.)
Since the simulation shows
with a sample proportion of
or
, we can conclude that
.
Since Bella's observed proportion of sixes in 100 rolls was 0.18, we need to compare this result to the range of proportions obtained from the simulation. If the observed proportion of 0.18 falls outside the range of proportions obtained from the simulation, then we have evidence to suggest that the die is not fair.
Looking at the table of proportions obtained from the simulation, we can see that the closest proportion to 0.18 is 0.15. If we assume that a fair die would produce a proportion of 0.167 (which is what we would expect if each of the six faces had an equal chance of coming up), then we can conclude that Bella's die may not be fair. However, since the sample size of 100 rolls is relatively small, we cannot be completely certain that the observed proportion of sixes is due to a biased die and not just random chance.
Therefore, the inference we can make from the simulation is that Bella's die may not be fair, but we cannot be completely certain based on this evidence alone.
There is an upcoming election for student council president at a high school. Candidate A must get over 50% of the vote to be elected. A poll was taken of a random sample of 50 students from the high school and 22 students said they would vote for Candidate A. Simulations were done with a population percentage of 50% and a sample size of 50 to see how likely a sample of 50 would have 22 who preferred Candidate A. The results of 200 simulations are shown below. What conclusion can be drawn regarding the likelihood that Candidate A will win the election with more than 50% of the vote?
Proportion who Prefer Candidate A
0.28
0.32
0.36
0.4
0.44
0.48
0.52
0.56
0.6
0.64
0.68
0.72
0.76
0.8
(Note: don't use percents as a sample proportion.)
Since the simulation shows
with a sample proportion of
or
, the results of the survey
.
Since the simulation shows a range of sample proportions for each population proportion, we can use it to determine how likely it is that a sample proportion of 22/50 (0.44) or higher would be obtained if the true proportion of students who prefer Candidate A is actually 50%. If the proportion of 0.44 falls within the range of proportions obtained from the simulation, then we can consider the result consistent with the hypothesis that Candidate A will win with over 50% of the vote. However, if the proportion of 0.44 falls outside of the range of proportions obtained from the simulation, then we have evidence to suggest that Candidate A may not win with over 50% of the vote.
Looking at the table of proportions obtained from the simulation, we can see that the closest proportion to 0.44 is 0.48. This suggests that it may not be very likely for Candidate A to win with over 50% of the vote based on the sample of 50 students who were surveyed. However, we would need to calculate the level of significance and conduct a hypothesis test to determine whether this result is statistically significant or not.
Therefore, the inference we can make from the simulation is that it may not be very likely for Candidate A to win with over 50% of the vote, but we cannot be completely certain based on this evidence alone. Further statistical analysis would be needed to make a more definitive conclusion.
The senior class president of a large university claimed that 75% of the senior class was interested in going on the senior trip. To test this claim, the senior class president conducted a survey of a random sample of 40 seniors and 21 said that they wanted to go on the senior trip. To better understand the significance of the survey results, a simulation was devised based on the claim that 75% of the seniors wanted to go on the trip, each of sample size 40, simulated 200 times. Explain how the results of the simulation can be used to support or refute the senior class president's claim.
Proportion of Students Interested in the Trip
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
(Note: don't use percents as a sample proportion.)
Since the simulation shows
with a sample proportion of
or
, the claim that 75% of the senior class wants to go on the senior trip is
.
Since the simulation shows a range of sample proportions for each proportion of students interested in the trip, we can use it to determine how likely it is that a sample proportion of 21/40 (0.525) or lower would be obtained if the true proportion of students interested in the trip was actually 75%. If the proportion of 0.525 falls outside the range of proportions obtained from the simulation, then we can consider the result inconsistent with the claim that 75% of the senior class wants to go on the senior trip.
Looking at the table of proportions obtained from the simulation, we can see that the closest proportion to 0.525 is 0.55. This suggests that it may not be very likely for 75% of the senior class to be interested in going on the senior trip given the sample of 40 seniors who were surveyed. Therefore, we have evidence to suggest that the senior class president's claim may not be accurate.
To determine whether this result is statistically significant or not, we would need to calculate the level of significance and conduct a hypothesis test. However, based on the simulation results alone, we can conclude that the claim that 75% of the senior class wants to go on the senior trip is unlikely to be true based on the sample of 40 seniors who were surveyed.
Therefore, the inference we can make from the simulation is that the senior class president's claim that 75% of the senior class wants to go on the senior trip is not supported by the survey results and may not be accurate.
Sarah rolled a die 40 times and 5 of the 40 rolls came up as a six. She wanted to see how likely a result of 5 sixes in 40 rolls would be with a fair die, so Sarah used a computer simulation to see the proportion of sixes in 40 rolls, repeated 200 times. Based on the results of the simulation, what inference can Sarah make regarding the fairness of the die?
Proportion of Sixes Rolled
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
(Note: don't use percents as a sample proportion.)
Since the simulation shows
with a sample proportion of
or
, we can conclude that
.
Since Sarah's observed proportion of sixes in 40 rolls was 0.125, we need to compare this result to the range of proportions obtained from the simulation. If the observed proportion of 0.125 falls within the range of proportions obtained from the simulation, then we have evidence to suggest that the die is fair and that Sarah's result is not unusual. However, if the observed proportion of 0.125 falls outside of the range of proportions obtained from the simulation, then we have evidence to suggest that the die may not be fair.
Looking at the table of proportions obtained from the simulation, we can see that the closest proportion to 0.125 is 0.1. This suggests that it may be somewhat unlikely for 5 sixes to come up in 40 rolls of a fair die. However, since the observed proportion is fairly close to some of the proportions obtained from the simulation, we cannot be completely certain that the die is biased based on this evidence alone.
Therefore, the inference we can make from the simulation is that it is somewhat unlikely for 5 sixes to come up in 40 rolls of a fair die, but we cannot be completely certain based on this evidence alone. Further statistical analysis would be needed to make a more definitive conclusion.
There is an upcoming election for student council president at a high school. Candidate A must get over 50% of the vote to be elected. A poll was taken of a random sample of 40 students from the high school and 23 students said they would vote for Candidate A. Simulations were done with a population percentage of 50% and a sample size of 40 to see how likely a sample of 40 would have 23 who preferred Candidate A. The results of 100 simulations are shown below. What conclusion can be drawn regarding the likelihood that Candidate A will win the election with more than 50% of the vote?
Proportion who Prefer Candidate A
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
(Note: don't use percents as a sample proportion.)
Since the simulation shows
with a sample proportion of
or
, the results of the survey
.