Stats 1.3 Assignment

Select the appropriate standardized statistics for each friend from the null distribution produced by applet.

-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)

Select the strongest and least strong evidence of the long-run proportion that the friend will choose scissors is less than 1/3.

-The strongest evidence is 65 out of 300 -The least strong evidence is 100 out of 400

Suppose that you were to generate the null distribution of the sample proportion of correct answers, that is, the distribution of possible values of sample proportion of correct identifications if Zwerg always guesses. Where would you anticipate this distribution would center, and will the SD of the null distribution be negative, positive, or 0?

0.5, because that is the value of the parameter if the null hypothesis is true. The standard deviation will be positive because the standard deviation must be at least 0, and is only equal to zero if there is no variability in the values (there will be variability in the simulated statistics).

When the null distribution of the sample proportion of correct answers is generated, where would you anticipate this distribution would center and will the standard deviation of the null distribution be negative, positive, or 0?

0.5, because that is the value of the parameter if the null hypothesis is true. The standard deviation will be positive because the standard deviation must be at least 0, and is only equal to zero if there is no variability in the values (there will be variability in the simulated statistics).

Use an applet to generate the null distribution of sample proportion of correct answers and use it to determine the standardized statistic. (Round answer to 2 decimal places, e.g. 52.75)

3.74

Which of the following null hypothesis and alternative hypothesis are appropriate in the context of the study?

Null: The long-run proportion of times that rhesus monkeys choose the correct box is 50%. ​Alt. The long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

Which of the following best defines the parameter of interest in the context of the study and uses the appropriate symbol?

The long-run proportion of times the lady correctly identifies which was poured first, π.

Which of the following is an appropriate result obtained from the data using standard deviation of the simulated statistics?

The number of standard deviations the observed proportion is above 0.50 in the null distribution.

Which of the following is the best interpretation of the standardized statistic in the context of this study?

The number of standard deviations the observed proportion is above 0.50 in the null distribution.

Interpret the meaning of the standardized statistic.

The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50.

Which of the following best describes what your standardized statistic means from the previous question?

The standardized statistic represents the number of standard deviations the observed proportion is above 0.5.

Select the best conclusion that you would draw about the research question of whether Zwerg does better than randomly guessing when the cue is that the experimenter points at the correct object.

We have strong evidence that the long-run proportion of times that Zwerg makes the correct choice is greater than 50%.

Select the best conclusion that you would draw about the research question of whether rhesus monkeys have some ability to understand gestures made by humans.

We have strong evidence that the long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

Select the best conclusion that you would draw about whether the lady does better than if she were just randomly guessing.

We have strong evidence that the long-run proportion of times that the lady makes the correct identification is greater than 50%.

Select the best conclusion that you would draw about the null and alternate hypotheses.

We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.

Which of the following best describes the null hypothesis and the alternative hypothesis using the appropriate symbol?

null: n(pi symbol)=0.5 , alternative: n(pi symbol) >0.5

Which of the following best describes the null hypothesis and the alternative hypothesis using the appropriate symbol?

null: p^=0.5, alternative: p^ <0.5

Which of the following best describes the null hypothesis and the alternative hypothesis using π?

null: π = 0.5, alternative: π > 0.5

What is the observed proportion of times the lady correctly identified what was poured first into the cup? What symbol should you use to represent this value? (Round answer to 0 decimal places, e.g. 5275.)

p^ 1

Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275)

p^=0.645

What is the observed proportion of times Zwerg picked the correct object? What symbol should you use to represent this value? (Round answer to 2 decimal places, e.g. 52.75)

p^=0.77

The symbol π represents the long-run proportion of all the couples that lean their heads _________while kissing

right

Determine the standardized statistic from the data. ​(Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75)

z=3.22