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Statistics Module 4 Solved 100% Correct, Exams of Statistics

Arizona State University (ASU) - TempeStatistics

Statistics Module 4 Solved 100% Correct

Typology: Exams

2023/2024

Available from 09/07/2024

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Statistics Module 4 Solved 100% Correct
95% confidence interval - ANSWER-he 95% confidence interval, for example, means
that 95% of the experiments with the given treatment will contain the true population
mean. Consequently, 5% (or 1 in 20) of the experiments will not contain the true
population mean. A 95% confidence interval implies that the researcher is 95%
confident that the population mean lies in the interval that is centered around the
sample mean.
95% confidence represents - ANSWER-range of values where you would fail to reject
the null hypothesis
A ______ test involves a directional hypothesis, whereas a ______ test involves a non-
directional hypothesis. - ANSWER-one-tailed,
two-tailed
A normal distribution can be defined by its ___ and ______. - ANSWER-mean and
standard deviation
A normal distribution can be defined by which of the following? - ANSWER-mean and
standard deviation
a range of values likely to contain the population parameter - ANSWER-confidence
interval
a range of values that is likely to contain the true population mean. - ANSWER-
confidence interval
A sample of n =12 is selected from a population whose mean is μ=80 (σ=12). After a
treatment is applied to the sample, the size of the treatment is d=0.25. What was the
sample mean?a. =79b. =81c. =83d. =85 - ANSWER-d=0.25
d= x-M/ sdev
x= d(sdev) + M
x= 83
C
a sample statistic that is used to estimate the population parameter e.g. x bar -
ANSWER-point estimate
an exact value that is observed - ANSWER-raw score
area under normal curve - ANSWER-total relative frequency
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Statistics Module 4 Solved 100% Correct

95% confidence interval - ANSWER-he 95% confidence interval, for example, means that 95% of the experiments with the given treatment will contain the true population mean. Consequently, 5% (or 1 in 20) of the experiments will not contain the true population mean. A 95% confidence interval implies that the researcher is 95% confident that the population mean lies in the interval that is centered around the sample mean. 95% confidence represents - ANSWER-range of values where you would fail to reject the null hypothesis A ______ test involves a directional hypothesis, whereas a ______ test involves a non- directional hypothesis. - ANSWER-one-tailed, two-tailed A normal distribution can be defined by its ___ and ______. - ANSWER-mean and standard deviation A normal distribution can be defined by which of the following? - ANSWER-mean and standard deviation a range of values likely to contain the population parameter - ANSWER-confidence interval a range of values that is likely to contain the true population mean. - ANSWER- confidence interval A sample of n =12 is selected from a population whose mean is μ=80 (σ=12). After a treatment is applied to the sample, the size of the treatment is d=0.25. What was the sample mean?a. =79b. =81c. =83d. =85 - ANSWER-d=0. d= x-M/ sdev x= d(sdev) + M x= 83 C a sample statistic that is used to estimate the population parameter e.g. x bar - ANSWER-point estimate an exact value that is observed - ANSWER-raw score area under normal curve - ANSWER-total relative frequency

Avid runners claim to run an average of 14 miles per week (σ = 1.5 miles). Researchers believe that the mean may be different than 14 miles. They select 60 avid runners. The sample mean was found to be 13.7 miles (s = 1.7 miles). Conduct a z-test with α = 0. to determine if there is evidence to conclude that the mean number of miles run each week by avid runners differs. Report your results in APA format. - ANSWER-1) State Hypotheses H0: μ = 14 milesHa: μ ≠ 14 miles

  1. Determine Critical Values Since this is a two-tailed test at α = 0.05, zcrit = ±1.96.
  2. Calculate the Test Statistic
  3. Compare and Decide Since z = -1.57 does not exceed the critical value of ±1.96, we fail to reject the null hypothesis. The result is not statistically significant.The results should be reported as follows:z = -1.57, p > 0.05, two-tailed Based on the 68-95-99.7 rule, what percentage of sample means lie within 2 standard deviations of the mean? - ANSWER-95% Calculate the z-score for sample mean - ANSWER-(x-M)/sdev/ sqrt(N) Comparing Values using z-Scores and Raw Scores When comparing z-scores from the same population or sample, it may be more meaningful to convert the z-score back to a raw score. For example, compare the performances of the following students on the physiology exam (μ = 87 , σ = 4 ) given the -scores listed below for Josef, Marco, and Brooklyn. Josef: z=-1. Marco: z=-2. Brooklyn: z=1.25 - ANSWER-Convert each z-score to a raw score. Then compare the raw scores. Josef: X=87 - 1.75(4) = 80 Marco: X= 87 - 2.50(4) = 77 Brooklyn: X= 87 + 1.25(4) = 92 Consider the example of the exam scores from Figure 4.3 ( μ = 75 , σ = 5 ). Suppose the teacher would like to know the proportion of scores on the exam that are below 65. - ANSWER-1. transform raw score to a z-score 2 use normal table to find the p-value for z score

H0: μ = 300 booksHa: μ < 300 books

  1. Determine Critical Values Since this is a left-sided test at α = 0.01, zcrit = -2.33.
  2. Calculate the Test Statistic
  3. Compare and Decide Since -3.68 exceeds the critical value of -2.33, it lies in the critical region. Therefore, reject the null hypothesis. The result is statistically significant. The results should be reported as follows:z = -3.68, p < 0.01, one-tailed. Power = 1 - Beta - ANSWER-In other words, if there is an effect, the power describes the likelihood that the study will provide evidence of the effect. Power is calculated prior to beginning a research study to define the probability of committing a Type II error (failing to reject a false null hypothesis) a value known as β. The statistical power of a study is measured on a scale of 0 to 1. Thus, researchers can calculate statistical power by using the following formula: Power = 1 - β Statistical power is effect, sample, size, significance level, number of tails of the test, and the type of hypothesis test used. Specifically, large effect sizes, large sample sizes, one-tailed tests, and higher significance levels tend to increase statistical power. T/F For a normal curve, the median, mean, and mode are typically equal T/F The area below the curve is 120%. - ANSWER-True False. 100% or 1. T/F Hypothesis testing can determine the absolute size of the effect of the treatment. It can determine whether the treatment caused a substantial effect - ANSWER-False. , it cannot determine the absolute size of the effect of the treatment. In other words, it cannot determine whether the treatment caused a substantial effect T/F large sample sizes tend to decrease statistical power - ANSWER-False. Tend to increase! T/F The greater the standard deviation, the less spread out the normal curve. - ANSWER-FALSE

The greater the standard deviation, the more spread out the normal curve. The smaller the standard deviation, the narrower the normal curve. the --___ rule con? - ANSWER-68-95-99. However, the rule only works when values are exactly 1, 2, or 3 standard deviations away from the mean. In order to apply the concept of proportions to other standard deviation values, such as σ = ± 1.4 or σ = ± 2.3, scores or values in the dataset must be standardized. the probability of committing a Type II error (failing to reject a false null hypothesis) - ANSWER-Beta the probability of correctly rejecting a null hypothesis that is false - ANSWER-statistical power What does a +z-score mean? what does a -z-score mean? - ANSWER-the value from the dataset lies above the mean the value from the dataset lies below the mean What is a confidence interval? - ANSWER-A confidence interval is a range of values that is likely to contain the true population mean. The 95% confidence level is the most common. What is effect size? - ANSWER-While hypothesis testing can determine statistical significance, effect size can tell us how meaningful or impactful a particular result is. What is the critical area? - ANSWER-The area under the curve containing extreme values that rarely occur in the distribution. If the test statistic falls in the critical region, the result is statistically significant and you reject the null hypothesis. What is the purpose of calculating z-scores? - ANSWER-The purpose is to understand a score's relative standing in the distribution. The z-score standardizes scores from different data sets with different means. What researchers calculate to determine the absolute magnitude, or size, of the treatment. One measure for this is... - ANSWER-effect size One measure for effect size is Cohen's d.