Does listening to music while studying hinder students’ learning? Two AP Statistics students designed an experiment to find out. They selected a random sample of 30 students from their medium-sized high school to participate. Each subject was given 10 minutes to memorize two different lists of 20 words, once while listening to music and once in silence. The order of the two-word lists was determined at random; so was the order of the treatments. The difference in the number of words recalled (music − silence) was recorded for each subject. A paired t-test on the differences yielded t = −3.01 and P-value = 0.0027.

(a) State appropriate hypotheses for the paired t-test. Be sure to define your parameter.

(b) What are the degrees of freedom for the paired t-test?

(c) Interpret the P-value in context. What conclusion should the students draw?

(d) Describe a Type I error and a Type II error in this setting. Which mistake could students have made based on your answer to part (c)?

(a) The appropriate hypotheses for the paired t-test in this experiment are:

Null hypothesis (H0): The mean difference in the number of words recalled between listening to music and silence is zero.

Alternative hypothesis (Ha): The mean difference in the number of words recalled between listening to music and silence is not zero.

Parameter: The parameter of interest is the mean difference in the number of words recalled (music - silence) for the population of students.

(b) The degrees of freedom for the paired t-test are calculated as (n - 1), where n is the number of paired observations. In this case, since there are 30 students in the sample, the degrees of freedom would be (30 - 1) = 29.

(c) The P-value of 0.0027 indicates the probability of observing a t-value as extreme as -3.01 (or more extreme) under the null hypothesis. In other words, if the null hypothesis were true (the mean difference is zero), there is only a 0.27% chance of obtaining a t-value as extreme as -3.01.

Since the P-value is less than the conventional significance level of 0.05 (or 5%), we reject the null hypothesis. Therefore, the students can conclude that listening to music while studying has a significant effect on the number of words recalled.

(d) In this setting:

- Type I error: This refers to rejecting the null hypothesis when it is actually true. It means concluding that there is a significant difference in the number of words recalled due to listening to music while studying when, in reality, there is no such difference.

- Type II error: This refers to failing to reject the null hypothesis when it is actually false. It means failing to conclude that there is a significant difference in the number of words recalled due to listening to music while studying when, in reality, there is a difference.

Based on the answer to part (c), the students rejected the null hypothesis and concluded that listening to music while studying has a significant effect on the number of words recalled. Therefore, if the null hypothesis were true (no actual difference), the students could have made a Type I error by incorrectly concluding that there is a difference.

In general, childcare workers should use their personal technological devices only when children are occupied or asleep.


True


False

Which best describes the physical and chemical digestion of food?

“Little Red Riding Hood” is what type of story?

fable

myth

legend

morality tale

Postini is a global company specializing in communications security. The company has
determined that 91% of all e-mails are actually spam. If you check your e-mail in the morning
and see that you have 25 new messages, what is the probability that:
a. (5 points) Exactly 5 of them are spam?
b. (5 points) Less than 20 of them are spam?
c. (5 points) Ten or more of them are spam?

Need Opinions, do you think that minimum wage is a reasonable and fair livable wage in the United States?

pleaseee on a timer
The Dahomey Amazons were such a large military force that, by the 1800s, the female warriors made up about one-third of the entire Dahomey army.

True

False

Terrence is playing with his four-year-old son Jacob, using a tablet app that records sounds from the environment. When they have recorded all the sounds they want, they can use the app to layer sounds over one another to create a mashup-like song. What are Terrence and Jacob doing together?


strengthening gross motor skills


creating not consuming


co-viewing


setting screen time limits

Sandy is the mother of a toddler at the childcare facility where you work. She has dropped off her son Nathan at the facility and it appears that he is sick—to make sure, you check his fever and find out that it is 102°. You call her to ask her about the situation, and she says that she knew he was sick, but she cannot miss work today, so he needs to stay at the center. Your facility’s sick child policy states that sick children with fevers over 101° need to stay home until 24 hours has passed from the time the fever went below 100°. How would you respond to Sandy in a way that maintains professionalism and a good relationship with her while still enforcing the sick child policy? Please write a verbatim “script” for what you could say to her.

Write a brief paragraph that articulates your analysis of picture. Support your analysis with evidence from the cartoon.