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In statistics, random samples are used to make generalizations, or inferences, about a population. Give a full correct answer for this question its true or false?

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2020-10-19

The correct answer is True because: A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.

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asked 2021-02-25

Give a full and correct answer Why is it important that a sample be random and representative when conducting hypothesis testing? Representative Sample vs. Random Sample: An Overview Economists and researchers seek to reduce sampling bias to near negligible levels when employing statistical analysis. Three basic characteristics in a sample reduce the chances of sampling bias and allow economists to make more confident inferences about a general population from the results obtained from the sample analysis or study: * Such samples must be representative of the chosen population studied. * They must be randomly chosen, meaning that each member of the larger population has an equal chance of being chosen. * They must be large enough so as not to skew the results. The optimal size of the sample group depends on the precise degree of confidence required for making an inference. Representative sampling and random sampling are two techniques used to help ensure data is free of bias. These sampling techniques are not mutually exclusive and, in fact, they are often used in tandem to reduce the degree of sampling error in an analysis and allow for greater confidence in making statistical inferences from the sample in regard to the larger group. Representative Sample A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study. A representative sample parallels key variables and characteristics of the large society under examination. Some examples include sex, age, education level, socioeconomic status (SES), or marital status. A larger sample size reduced sampling error and increases the likelihood that the sample accurately reflects the target population. Random Sample A random sample is a group or set chosen from a larger population or group of factors of instances in a random manner that allows for each member of the larger group to have an equal chance of being chosen. A random sample is meant to be an unbiased representation of the larger population. It is considered a fair way to select a sample from a larger population since every member of the population has an equal chance of getting selected. Special Considerations: People collecting samples need to ensure that bias is minimized. Representative sampling is one of the key methods of achieving this because such samples replicate as closely as possible elements of the larger population under study. This alone, however, is not enough to make the sampling bias negligible. Combining the random sampling technique with the representative sampling method reduces bias further because no specific member of the representative population has a greater chance of selection into the sample than any other. Summarize this article in 250 words.

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asked 2020-11-03

The sampling distribution of \(\frac{S_{1}^{2}}{S_{2}^{2}}\) is the \(\chi^2 \) distribution. Give a correct answer true or false inference for two population variances is done through their difference.

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asked 2021-01-28

Indicate true or false for the following statements. If false, specify what change will make the statement true.
a) In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase.
b) When the means of two independent samples are used to to compare two population means, we are dealing with dependent (paired) samples.
c) The \(\displaystyle{x}^{{{2}}}\) distribution is used for making inferences about two population variances.
d) The standard normal (z) score may be used for inferences concerning population proportions.
e) The F distribution is symmetric and has a mean of 0.
f) The pooled variance estimate is used when comparing means of two populations using independent samples.
g) It is not necessary to have equal sample sizes for the paired t test.

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asked 2020-10-18

Give full and correct answer for this question, the chi-square test can be used: Select one: a. to make inference about a population mean. b. to test for survey error. c. to compare more than two independent proportions. d. for pairwise multiple comparisons of means. e. to test for difference in two variances.

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asked 2021-01-05

Give full and correct answer for this questions 1) A t-test is a ? 2) Which of the following statement is true? a)The less likely one is to commit a type I error, the more likely one is to commit a type II error, b) A type I error has occurred when a false null hypothesis has been wrongly accepted. c) A type I error has occurred when a two-tailed test has been performed instead of a one-tailed test, d) None of the above statements is true. 3)Regarding the Central Limit Theorem, which of the following statement is NOT true? a.The mean of the population of sample means taken from a population is equal to the mean of the original population. b. The frequency distribution of the population of sample means taken from a population that is not normally distributed will approach normality as the sample size increases. c. The standard deviation of the population of sample means is equal to the standard deviation of the, original population. d. The frequency distribution of the population of sample means taken from a population that is not normally distributed will show less dispersion as the sample size increases.

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asked 2021-01-10

GIve a correct answer for this question: when we are comparing two population means from two groups (suppose they are called Group 1 and Group 2), which of the following statistics do we use to make a confidence interval or perform a hypothesis test for a difference in means?