What role does probability play in data analysis?

Group of answer choices

a) The same sample of numbers produces different answers depending on what statistics are used

b) Probability tells us the chances our sample reflects the true population parameter

c) We randomly choose what analysis to conduct

d) Data analysis is only good for understanding gambling problems

Researchers at NMSU would like to estimate the proportion of NMSU students who participate in online gambling. They randomly sample 250 students and ask them about online gambling. From the data, the researchers found that 4.7% of respondents participate in online gambling.

What is the parameter in the study?

Group of answer choices

a)The question the students were asked to respond to

b)The proportion of NMSU students who participate in online gambling

c)4.7% of respondents that participate in online gambling

d)250 students

Which of the following statements about the p-value is true?

Group of answer choices

a) As the effect size increases, the p-value decreases

b) As the sample size increases, the p-value increases

c) The p-value must always be below 0.05.

d)As the p-value increases, we have more evidence against the null hypothes

Which of the following is an advantage of confidence intervals over hypothesis tests?

Group of answer choices

a) Confidence intervals do not require subject knowledge about the size of an estimate

b)Confidence intervals are not affected by the variation in the data

c) Confidence intervals provide a range of values rather than a binary decision

d) Confidence intervals use probability to make a decision, which is more intuitive

A marketing firm randomly sampled 800 New Mexicans and 1000 Arizonans and asked them how much they paid last month for electricity. The data show that the New Mexican respondents paid an average of $23 more per month on electricity than the Arizonan respondents. The 95% confidence interval for the difference is (-0.56, 46.56).

What can you conclude about the amount paid last month by all New Mexicans compared to the amount paid by all Arizonans?

Group of answer choices

a) New Mexicans paid more than Arizonans because the difference of $23 is practically significant

b) We cannot say whether New Mexicans paid more or less than Arizonans at the 95% level

c) New Mexicans likely paid more than Arizonans because the the interval is mostly above zero

d) We cannot conclude there's a difference at 95%, but we probably would if we increased the confidence level to 99%

Which of the following statements correctly describes the behavior of the width of a confidence interval?

Group of answer choices

a) As the standard error increases, the width of the confidence interval decreases

b) As the confidence level increases, the width of the interval decreases

c) As the sample size increases, the width of the confidence interval decreases

d) The width of the confidence interval is not affected by the variation in the data