Analytics Test Study Guide

Suppose that 45% of all adult women think they do not get enough time for themselves. An opinion poll interviews 1000 randomly chosen women and records the sample proportion, 𝑝̂, who feel they don't get enough time for themselves. (i) What is the mean of the sampling distribution of 𝑝̂ ? and (ii) What can you tell about the distribution of 𝑝̂ ?

(i)sample mean= 0.45 (ii) Normal

The standard normal distribution has a mean and a standard deviation respectively equal to

0 and 1

Which of the following values is not typically used for α? 0.50 0.01 0.10 0.05

0.50

If we plot a continuous probability distribution f(x), the total probability under the curve is

1

A sample o size 100 has a standard deviation of 20. What is the standard deviation of the sample mean (standard error)?

20/Sqrt(100) = 2

Which sign is possible in an alternative hypothesis? ≠ > < All of these signs are possible

All of these signs are possible

The margin of error for a confidence interval for the population mean µ increases as the sample size increases. T or F

False margin of error=2s/√n So as sample size n increases in the denominator the margin of error decreases.

Suppose a financial analyst wants to test the research hypothesis that stock prices average less in January than in the preceding December. Each data point (that is, each row in the data set) will include the average January daily closing price and the average December daily closing price for some stock for some December-January period, such as IBM's averages for December 2014 and January 2015. Which of the following is the best conclusion?

If the analyst gathers a huge sample of data points, there is a good possibility of finding a statistically significant result that is not practically significant.

If for covid-19 testing, we consider the population with age subgroups (children-young adults- adults- seniors) and assume that every subgroup is homogenous and then sample from every age subgroup, what is this sampling method called?

Stratified Sampling In stratified sampling, population is divided into relatively homogenous subgroups ("strata").

A company has recently changed its quality assurance program, with the goal of having fewer of its products fail under warranty. Past records, prior to the change, show that 3.45% of the company's products failed under warranty. A more recent random sample, after the change, show that 3 products out of 190 failed under warranty. Which of the following is true about the alternative hypothesis that the new proportion of failures under warranty is less than the previous proportion?

The null can be rejected in favor of the alternative at the 10% significance level, but not at the 5% significance level.

Suppose a study claims that the results are significant at the 1% significance level. Which of the following does this not imply?

The observed results would be very unlikely if the alternative hypothesis were true.

You want to test the null hypothesis that the difference between two population means is less than or equal to 0 versus a one-tailed alternative. Based on random samples from the two populations, you first calculate a 95% confidence interval for the mean difference, and it extends from 2.73 to 5.91. Which of the following is true?

The p-value for a two-tailed alternative must be less than 0.05, so the p-value for the one-tailed test you are running must be less than half this, i.e., less than 0.025.

Which of the following statements is least accurate? If the p-value is close to 1, there is virtually no evidence in support of the alternative hypothesis. A test statistic not in the rejection region indicates a lack of support for the alternative hypothesis. The p-value is the probability that the alternative hypothesis is true. A statistically significant result is evidence that the null hypothesis is false.

The p-value is the probability that the alternative hypothesis is true.

A university has calculated a 95% confidence interval for the population mean height µ of 22-year old males at their school. They found it to be 69± 2 inches.If they took many additional random samples of the same size and from each computed a 95% confidence interval for µ, approximately 95% of these intervals would contain the population mean µ. T or F

True

Non-sampling error is a term used in statistics that refers to an error that occurs during data collection (from sources other than luck of the draw), causing the data to differ from the true values. T or F

True

The standard error of large samples tends to be less than the standard error for small samples. T or F

True

For a sample size of 100, all sampling distribution of sample mean approach normal distribution regardless of the true distribution of parent population. T or F

True (This is based on Central Limit Theorem)

Which equation shows the process of standardizing?

Z = (X - μ)/σ

A 95% confidence interval can be used to reject the null hypothesis of a two-sided test at the 5% significance level if and only if

a 95% confidence interval does not include the hypothesized value of the parameter.

A continuous probability distribution is characterized by

a continuum of possible values.

The mean μ of a probability distribution is a measure of

central location.

The normal distribution is a

continuous distribution with two parameters.

For a certain type of battery, the lifetimes of batteries follows a Normal distribution with mean 10 hours and standard deviation 0.6 hours. What are the mean and standard deviation of the sampling distribution of x¯ for a random sample of 60 batteries?

mean=10, standard error=0.08

A type I error occurs when the

null hypothesis is incorrectly rejected when it is true.

Larger p-values indicate more evidence in support of the

null hypothesis.

A teacher who is trying to determine if the evidence supports the fact that a new method of teaching economics is more effective than a traditional one will conduct a _____ test.

one-tailed

The null and alternative hypotheses divide all possibilities into

two non-overlapping sets.

The standard deviation σ of a probability distribution is a measure of

variability of the distribution.