W#4 NOTE Stats Lit #4

docx

School

Fairleigh Dickinson University *

*We aren’t endorsed by this school

Course

2023

Subject

Statistics

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by mlle445

Wit4 NOTE Stats Lit #4 Question 1 1 out of 1 points (Extra Credit) Let's continue briefly with a biographical sketch from design of experiments before beginning inferential statistics. Can Sir Ronald Fisher arguably be called "the father of statistics"? Among other, Professor Emeritus David S. Moore of Purdue University grants him this honor, due in no small part to his design of random comparative experiments, perhaps his greatest contribution to what was an evolving discipline in his time. His field experiments were focused on agricultural improvements through the use of innovative statisitcal design. Seem reasonable? Check into his biographical details if still curious, or, pardon the pun, uncertain. Agree or Disagree? Selected Answer: Agree Question 2 1 out of 1 points The empirical rule associated with normal curves in general and the standard normal probability distribution in particular provides an initial glimpse into the concept of statistical confidence. For example, according to the empirical rule, 68.27% of all samples taken from a normally distributed population should have sample means within one (1) standard deviation of the true population mean or parameter. Similarly, 95.45% of all samples taken from a normally distributed population should have sample means within two (2) standard deviations of the true population mean or parameter. Furthermore, 99.73% of all samples taken from a normally distributed population should have sample means within three (3) standard deviations of the true population mean or parameter. FALSE or TRUE? Selected Answer: True Question 3 1 out of 1 points A confidence interval for a population parameter identifies an interval within which the likelihood of that interval containing the true population parameter is a certain or specified probability. FALSE or TRUE? Selected Answer: True Question 4 1 out of 1 points The confidence interval should be based on an SRS or simple random sample of size n taken from a population with population mean, g, unknown but population standard deviation, & , known. FALSE or TRUE? Selected Answer: True Question 5 1 out of 1 points - c The confidence interval where the parameter being estimated is the population mean, i, can be symbolized as follows: x + z——. n The standard normal or standardized score, z, represents the absolute value of a one-tail critical value. FALSE or TRUE? Selected Answer: True Question 6 1 out of 1 points Critical values are standardized scores, such as z-scores, that designate or cut off specific areas under the tail section(s) of a density curve for a probability distribution. There can be one or two critical values: one for the lower or left tail; one for the upper or right tail, or two which are for both the lower and upper tails. The number of critical values depend on the type of statistical inference being conducted and claims being considered. FALSE or TRUE? Selected Answer: True

Question 7 1 out of 1 points The margin of error is a statistic; it expresses the quantity or amount of error among outcomes when randomly sampling. The error is the difference between the observed statistical results and the reality that is the true parametric value. FALSE or TRUE? Selected Answer: True Question 8 1 out of 1 points The margin of error gets smaller when the population standard deviation, ¢, gets smaller and/or the sample size, n, gets larger. FALSE or TRUE? Selected Answer: True Question 9 1 out of 1 points The margin of error associated with confidence intervals estimating a single population's mean can be symbolized as follows: z n Again, z is a one-tail critical value, but is sometimes referred to z-sub-alpha-over-two, based off a two tail scenario and a significance level, @. Symbolically, that is written as z o /2. FALSE or TRUE? Selected Answer: True Question 10 1 out of 1 points The level of significance, a, is another label for a Type | error, or the chance of rejecting a null hypothesis when in fact it is true. FALSE or TRUE? Selected Answer: True Question 11 1 out of 1 points The confidence level is represented as 1 — a. FALSE or TRUE? Selected Answer: True Question 12 1 out of 1 points 70 )2 When estimated a population mean, the minimum sample size necessary can be determined as follows: n= (E Let E represent the error amount. FALSE or TRUE? Selected Answer: True

Question Question Question Question Question Question Question Question Question 13 1 out of 1 points Hypothesis testing is a main technique for conducting statistical inference to check whether any differences exist between conjectures and observation or outcomes; in other words, sample statistics are utilized to test population parameters. Statistically interesting findings from these tests are called significant when the results are very unlikely to have occured by chance. FALSE or TRUE? Selected Answer: True 14 1 out of 1 points xX—p Fpr hypothesis testing involving the parameter, u, for a single population, the form of the test statistic is as follows: z=——. - / Y FALSE or TRUE? Selected Answer: True 15 1 out of 1 points Hypothesis testing can be one-sided if the inequality associated with the alternative hypothesis is directional -- less than or greater than, or two-sided if non-directional -- strictly not equal. One-sided tests can be left-tail or right tail, depending on the sense of the inequality and the problem context; two-sided tests are two tailed. FALSE or TRUE? Selected Answer: True 16 1 out of 1 points Findings that are technically statistically interesting are called significant when the results are very unlikely to have occurred by chance. When the occurrence of a particular sample statistic generated by the testing of hypotheses is essentially too unusual or rare to have happened randomly, the findings can be deemed significant. However, such results always have an included error component, so they are not unfortunately a guarantee conclusions are correct or incorrect. FALSE or TRUE? Selected Answer: True 17 1 out of 1 points The null hypothesis is a statistically-based claim that there is no effect or change to the population being studied, based on some experiment or intervention being conducted or considered. FALSE or TRUE? Selected Answer: True 18 1 out of 1 points The alternative hypothesis is the statistically-based counter claim that there indeed is some effect or change to the population being studied. It is also called the research hypothesis, and can sometimes be framed as the complimentary event to the null hypothesis. FALSE or TRUE? Selected Answer: True 19 1 out of 1 points The p-value is a probability that represents the likelihood of the observed outcome happening when the null hypothesis is in fact true. In cases where the test statistic from the sample is far removed from and more extreme than the actual population parameter, the p-value would be relatively small, perhaps smaller than the level of significance. FALSE or TRUE? Selected Answer: True 20 1 out of 1 points When the p-value of a statistical test is smaller than the level of significance, a, then the results are statistically significant. FALSE or TRUE? Selected Answer: True 21 1 out of 1 points As a p-value decreases in size, the strength of the evidence against the null hypothesis increases. FALSE or TRUE? Selected Answer: True

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 22 1 out of 1 points A hypothesis test is significant, or results in significant findings, when its outcome is sufficiently unlikely to occur, less likely and therefore a smaller chance of occurrence than some predetermined acceptable probability for making an error, which is known as the level of significance, a. FALSE or TRUE? Selected Answer: True Question 23 1 out of 1 points Confidence intervals are an alternative approach to testing hypotheses. When the hypothesized population parameter, u, falls outside the confidence interval as determined by its confidence level, 1 — @, the null hypothesis is rejected. FALSE or TRUE? Selected Answer: True Question 24 1 out of 1 points A Type | error occurs in hypothesis testing when the null hypothesis is rejected and the alternative hypothesis is, by default, accepted as appropriate, but the null was indeed true. FALSE or TRUE? Selected Answer: True Question 25 1 out of 1 points A Type I error, symbolized by 3, occurs in hypothesis testing when the null hypothesis is accepted, or the researcher fails to reject it. The alternative hypothesis is rejected but it is indeed true. FALSE or TRUE? Selected Answer: True Question 26 1 out of 1 points The power of a test against a particular alternative value for the parameter when it is indeed true is computed as one minus the probability of a Type Il error, or 1 — . FALSE or TRUE? Selected Answer: True Question 27 1 out of 1 points Ending with more from design of experiments: The Hawthorne effect is witnessed when some intervention occurs under overt observation, causing statistically significant findings in the short term, which ultimately, are not sustained. Participant knowledge about the intervention biases the results and tampers with findings. FALSE or TRUE? Selected Answer: True

W#4 NOTE Stats Lit #4

Related Documents