Stats 1.2 Assignment

Use an applet to conduct a simulation with π = 0.5, n = 40, and number of repetitions = 1000. We find the proportion of times a value greater than or equal to 28 is observed. The p-value is approximately

0.008

Which is the most valid p-value?

0.23 (23 dots are 0.60 or larger)

What is the smallest proportion of times Hope could go toward the correct object so that you would have strong evidence that Hope understands pointing towards an object?

0.70

What is the observed value of the statistic in this case? (Round your answer to 3 decimal places; e.g. 5.275.)

0.875

It turned out that for 28 of the 40 couples in the sample (after the 7 couples who could not agree were excluded), the man said "I love you" before the woman did. ​​What is the sample proportion of couples for whom the man was the first to say "I love you"? What symbol is used to denote this statistic?

28/40 = 0.7 is the sample proportion; the symbol p-hat denotes this quantity.

What is the sample proportion of monkeys who picked the box towards which the human had gestured? Is this value a parameter or a statistic? What is the symbol you should use to denote this proportion?

30/40 = 0.75; statistic; we use the symbol p^ to denote this quantity

What is the sample proportion of monkeys who picked the box towards which the human had gestured. Is this value a parameter or a statistic? What is the symbol you should use to denote this proportion?

31/40 = 0.775; statistic. We use the symbol p^ to denote this quantity

It turned out that for 59 of the 96 responses, the man said "I love you" before the woman did. What is the sample proportion of couples for whom the man was the first to say "I love you" and what symbol do we use to denote this proportion?

59/96 = 0.61 is the sample proportion; we use the symbol p-hat to denote this quantity.

To use a coin-flipping model to find the p-value for these data, flip a coin

96 times and keep track of the number of heads. Repeat this process many times, keeping track of the number of heads each time.

Which of the following best describes how you could use a coin-flipping model to determine the p-value for this situation?

Flip a coin 40 times and keep track of the number of heads. Repeat the 40 coin flips 1000 times. Calculate the proportion of sets of 40 coin flips where 28 or more heads were obtained. That proportion is the p-value.

Consider how you could use a coin to conduct a simulation analysis of this study and its result.

Flip a coin 40 times and record the number of heads. Repeat this process of creating values for the number of heads recorded for each set of 40 tosses 999 more times, yielding a set of 1000 values of the number of heads received in 40 coin tosses. Compute the p-value as the proportion of times 30 or more heads were recorded by chance in the 1000 sets of 40 coin tosses. If the p-value is small, then this is convincing evidence that rhesus monkeys can interpret human gestures better than by random chance.

Consider how you could use a coin to conduct a simulation analysis of this study and its result.

Flip a coin 40 times and record the number of heads. Repeat this process of creating values for the number of heads recorded for each set of 40 tosses 999 more times, yielding a set of 1000 values of the number of heads received in 40 coin tosses. Compute the p-value as the proportion of times 31 or larger was obtained by chance in the 1000 sets of 40 coin tosses. If the p-value is small, then this is convincing evidence that rhesus monkeys can interpret human gestures better than by random chance.

represent the null and alternative hypotheses in symbols.

Ho: pi=0.5, Ha: pi > 0.5

Which of the following best describes the meaning of the p-value in this situation?

If Sarah doesn't understand how to solve problems and is just guessing at which picture to select, the probability she would get 7 or more correct out of 8 is 0.04.

A newspaper article described the 0.51 probability in the following manner: This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times. What is wrong with this statement?

In the long run it will land heads up 51% of the time; in any particular set of 100 flips it is likely the coin won't land heads up exactly 51 out of 100 times.

What does a single dot in the null distribution represent in terms of Sarah and the photos?

NOT!!!!! the proportion of the time that Sarah would choose the correct picture (out of 8) if she understood how to solve problems

Does the p-value indicate strong evidence that Hope understands pointing?

No, the approximate p-value is 0.23, which provides little to no evidence that Hope understands pointing.

Which of the following describes the best null and alternate hypotheses?

Null hypothesis: The long-run proportion of times that rhesus monkeys make the correct choice when observing the researcher jerk their head is 50% (just guessing). Alt hypothesis: The long-run proportion of times that rhesus monkeys make the correct choice is more than 50%. H0: π = 0.5, Ha: π > 0.5

Which of the following explains the null and alternative hypotheses?

Null hypothesis: The long-run proportion of times that rhesus monkeys make the correct choice when the researcher looks towards the correct box is 50% (just guessing). ​Alt hypothesis: The long-run proportion of times that rhesus monkeys make the correct choice is more than 50%. H0: π = 0.5, Ha: π > 0.5

Suppose you focused on the proportion of times the coin landed tails up instead of heads up. How would your hypotheses be different? What would you do differently to calculate your p-value?

Null would be the same, alternative would be > 0.5. To calculate the p-value, find the probability that 29 or larger (58% or larger) occurred.

Which of the following explains the null and alternative hypotheses?

Null: The long-run proportion of times Hope will go to the correct object is 0.50, ​Alt: The long-run proportion of times that Hope will go to the correct object is more than 0.50

Which of the following represents the null and alternative hypotheses?

Null: The long-run proportion of times Sarah chooses the correct photo is 0.5; H0: π= 0.5 ​Alt: The long-run proportion of times Sarah chooses the correct photo is more than 0.5; Ha: π > 0.5

Which of the following describes the best null and alternative hypotheses regarding if males are more likely to say "I love you" first?

Null: The proportion of all couples where the male said "I love you" first is 0.50. Alt: The proportion of all couples where the male said "I love you" first is greater than 0.50

Which of the following describes the best null and alternative hypotheses?

Null: The proportion of all couples where the male said "I love you" first is 0.50. Alt: The proportion of all couples where the male said "I love you" first is greater than 0.50

Select the best simulation using a six-sided die where the sample size is 20 and the null hypothesis probability is 1/6.

Roll a die 20 times, and keep track of how many times 'one' is rolled. Repeat this many times.

Which explains a simulation using a six-sided die where the sample size is 30 and the null hypothesis probability is 1/6?

Roll a die 30 times, and keep track of how many times 'one' is rolled. Repeat this many times.

We conducted a test of significance using the One Proportion applet and got the following null distribution for the "number of heads." Based on the null distribution, what is the p-value for the test? How did you calculate it? ​ Probability of heads: 0.5 Number of tosses: 8 Number of repetitions: 100 Total = 100

Since 4 of the 100 simulated outcomes gave a result of 7 or more, the p-value is 0.04.

Use an applet to conduct a simulation analysis with 1000 repetitions. Select the best way to explain whether rhesus monkeys have some ability to understand gestures made by humans and which p-value is the most valid.

The approximate p-value from the applet is 0.001. This small p-value means that 30 of the 40 monkeys pointing to the correct box is strong evidence that the rhesus monkeys are not guessing, which may lead us to believe that rhesus monkeys may be able to understand a head jerk to indicate which box to choose.

Use an applet to conduct a simulation analysis with at least 1000 repetitions based on the null distribution. Explain whether rhesus monkeys have some ability to understand gestures made by humans. Which p-value is the most valid?

The approximate p-value from the applet is 0.001. This small p-value means that 31 of the 40 monkeys pointing to the correct box is strong evidence that the rhesus monkeys are not guessing, which may lead us to believe that rhesus monkeys can interpret gestures to indicate which box to choose.

Use an applet to conduct a simulation with at least 1000 repetitions. Which p-value is the most valid?

The p-value is 0.16; there is little to no evidence that a spun penny lands heads up less than 50% of the time.

Use an applet to conduct a simulation with at least 1000 repetitions. Which p-value is the most valid?

The p-value is approximately 0.31. There is little to no evidence that a coin that starts out heads up will land heads up more than 50% of the time.

Select the interpretation of this p-value with the probability and hypothesis assumption.

The p-value is the probability of observing a value of 28 or greater, assuming that for 50% of couples the man said "I love you" first.

Select the best simulation using a set of five black cards and one red card where the sample size is 20 and the null hypothesis probability is 1/6.

Using a set of five black cards and one red card, shuffle the cards and choose a card. Note the color of the card and return it to the deck. Shuffle and choose a card 20 times keeping track of how many times the red card is selected. Repeat this many times.

Which of the following best describes the simulation using playing cards when the sample size is 20 and the null hypothesis probability is 2/3?

Using a set of one black card and two red cards, shuffle and choose a card 20 times keeping track of how many times a red card is selected. Repeat this many times.

Based on the p-value, what can be said about Sarah's ability to understand how to solve problems similar to those she was presented?

We have strong evidence that Sarah is not simply guessing, since 7 out 8 rarely occurs by chance (if just guessing).

How would you answer to (b) change if the sample size was 30?

You would have to choose a card 30 times instead of 20 times, and repeat many times.

What does Ha represent?

alternative hypothesis

The 40 heterosexual couples who agreed on their response to which person was the first to say "I love you" are the observational units. Whether the man or woman said "I love you" first is a

categorial variable

The symbol π in this context stands for the long-term proportion of all______________ where the man said "I love you" first.

couples

Assuming you have not found strong evidence that it will land heads up more than 50% of the time in the long run, what would be your verdict on Diacon's assertion that it will land heads up 51% of the time in the long run?

false

The symbol π in this context stands for the long-run proportion of the time that a spun penny lands on

heads

The symbol π in this context stands for the__________________ of times that Sarah chooses the correct photo.

long-run proportion

What does π represent?

long-run proportion (parameter)

The symbol π in this context stands for the

long-run proportion of times that the monkey will make the correct choice

What does H0 represent?

null hypothesis

Which of the following describes the best null and alternative hypotheses?

null: π = 0.50, alternative: π > 0.50

Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.

observational units are the monkeys; the variable is if the money approached the correct box or not, categorial

Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.

observational units are the monkeys; the variable is which box the monkey approached, categorial

Which of the following best describes what a single dot represents in the null distribution shown?

one possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object 50% of the time in the long run

Use an applet to conduct a simulation analysis to assess the strength of evidence against the null hypothesis. Which p-value is the most valid?

probability of heads: 0.5, number of tosses: 96, number of repetitions: 1000, as extreme as ≥ 0.61; yields a p-value of approximately 0.016

What does p^ represent?

sample proportion

What does n represent?

sample size

we have ____________ evidence that the long-run proportion of university student relationships in which the man says "I love you" first is more than 50%.

strong

The small p-value gives us

strong evidence that for more than 50% of couples the man said "I love you" first.

The symbol π in this context stands for the

the long-run proportion of times that the monkey will make the correct choice

Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.

the observational units are the couples; the variable is whether the male of female said "I love you first", categorial

The p-value in this scenario is the probability of observing the proportion 0.61 or larger assuming the null hypothesis is

true