126_S&P_Sneha

A coin is flipped 50 times, and it lands heads 35 times. A simulation assuming the coin is fair was conducted 1,000 times, and in 50 of those trials, the number of heads was 35 or more.

Does the simulation suggest the coin is biased at the 5% significance level?

• Yes, because 35 heads is unusual for a fair coin.

• No, because 50 out of 1,000 is greater than 5%.

• Yes, because the observed outcome occurs less than 5% of the time.

• No, because 5% is larger than 50 out of 1,000.

Two groups were surveyed about their favorite beverage:

• Group A: 70% preferred coffee.

• Group B: 60% preferred coffee.

A simulation randomly shuffled beverage preferences between the two groups 1,000 times, and the observed difference in proportions (10%) occurred in only 20 of the trials.

What conclusion can be drawn about the significance of the difference?

• The difference is significant because 20 out of 1,000 is smaller than 5%.

• The difference is not significant because 20 out of 1,000 is greater than 5%.

• The difference is significant because 10% is too large to occur by chance.

• The difference is not significant because 5% is smaller than 20 out of 1,000.

A researcher measured the height of plants grown using two types of fertilizer:

• Fertilizer A: Mean height = 23 cm

• Fertilizer B: Mean height = 25 cm

The researcher ran a simulation by shuffling the heights between the two groups 1,000 times. In 15 of those simulations, the mean difference was equal to or greater than 2 cm.

What is the conclusion about the difference at the 1% significance level?

• The difference is significant because 15 out of 1,000 is less than 1%.

• The difference is not significant because 15 out of 1,000 is greater than 1%.

• The difference is significant because the observed difference is rare.

• The difference is not significant because 2 cm is too small.

Machine A takes on average 10 minutes to produce a part, and Machine B takes on average 11 minutes. A simulation runs 2,000 trials where the processing time for parts is shuffled between the two machines, and in 90 trials, the observed difference in processing times was equal to or greater than 1 minute.

At the 10% significance level, is the difference statistically significant?

• Yes, because 90 out of 2,000 is less than 10%.

• No, because 90 out of 2,000 is greater than 10%.

• Yes, because the observed difference is rare.

• No, because the observed difference is within the expected range.

The variability of exam scores in two classes, Class A and Class B, is compared. A simulation is run 500 times to compare their standard deviations. The simulation shows that the observed difference in standard deviations (3 points) was exceeded in only 12 simulations.

At the 2% significance level, what conclusion can be drawn?

• The difference in variability is statistically significant, and we reject the null hypothesis.

• The difference in variability is not statistically significant, and we fail to reject the null hypothesis.

• The difference is significant, and the variability in Class B is greater than in Class A.

• There is not enough information to make a conclusion about variability.

A simulation of 1,000 trials is run to compare the means of two groups. The resulting distribution of mean differences has a mean of 0.5 and a standard deviation of 2. The observed difference in the means of the two groups is 4.

What can be concluded from this distribution?

• The observed difference is likely to be significant, as it is greater than the mean of the distribution.

• The observed difference is likely to be insignificant, as it falls within the expected range of the distribution.

• The observed difference is so large that it is guaranteed to be statistically significant.

• The observed difference is not important unless the p-value is calculated.

A researcher observes that, in 100 trials, the number of heads in a series of coin flips is more than 60% heads in 15 cases. The researcher runs a simulation of 1,000 trials to determine the likelihood of this result. The simulation shows that the observed result occurs in only 3% of the trials.

What can be concluded about the pattern of heads in the coin flips?

• The pattern is significant, suggesting the coin may be biased.

• The pattern is not significant, as it is consistent with random variation.

• The pattern indicates the coin is fair.

• There is not enough data to determine the significance.

A teacher compares the exam scores of two classes:

• Class A: Mean score = 72

• Class B: Mean score = 75

A simulation of random assignments of scores between the two groups (1,500 simulations) showed that the difference of 3 points or greater occurred in 45 of those trials.

At the 3% significance level, is the difference statistically significant?

• Yes, because 45 out of 1,500 is less than 3%.

• No, because 45 out of 1,500 is greater than 3%.

• Yes, because the observed difference is rare.

• No, because the observed difference is within the expected range.

A researcher randomly selects 100 people from a city to determine the proportion who prefer a certain brand of soda. After running 1,000 simulations of 100 random selections, the mean proportion of soda preference is 0.45, with a standard deviation of 0.05. The observed proportion of 0.50 is compared to this simulation result.

• The observed proportion of 0.50 is significantly different from the mean of 0.45.

• The observed proportion of 0.50 is within the expected range of random variation.

• The observed proportion of 0.50 is too large to be random.

• The simulation does not provide enough data to make a conclusion.

A teacher evaluates the performance of two math classes:

• Class X: Mean score = 68

• Class Y: Mean score = 70

A simulation of random assignments of scores between the two groups (2,000 simulations) showed that a difference of 2 points or more occurred in 80 of those trials.
At the 5% significance level, is the difference statistically significant?

• Yes, because 80 out of 2,000 is less than 5%.

• No, because 80 out of 2,000 is greater than 5%.

• Yes, because the observed difference is not common.

• No, because the observed difference is expected.