It is not necessary while comparing two means that the two sample sizes must be equal.

Question

asked 2021-01-27

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}&{H}{o}{u}{s}{e}{w}{\quad\text{or}\quad}{k}{H}{o}{u}{r}{s}\backslash{h}{l}\in{e}{G}{e}{n}{d}{e}{r}&{S}{a}\mp\le\ {S}{i}{z}{e}&{M}{e}{a}{n}&{S}{\tan{{d}}}{a}{r}{d}\ {D}{e}{v}{i}{a}{t}{i}{o}{n}\backslash{h}{l}\in{e}{W}{o}{m}{e}{n}&{473473}&{33.133}{.1}&{14.214}{.2}\backslash{h}{l}\in{e}{M}{e}{n}&{488488}&{18.618}{.6}&{15.715}{.7}\backslash{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
a. Based on this study, calculate how many more hours per week, on the average, women spend on housework than men.
b. Find the standard error for comparing the means. What factor causes the standard error to be small compared to the sample standard deviations for the two groups?
The cause the standard error to be small compared to the sample standard deviations for the two groups.
c. Calculate the 95% confidence interval comparing the population means for women
Interpret the result including the relevance of 0 being within the interval or not.
The 95% confidence interval for
\(\displaystyle{\left(\mu_{{W}}-\mu_{{M}}\right)}\)
is: (Round to two decimal places as needed.)
The values in the 95% confidence interval
are less than 0,
are greater than 0,
include 0,
which implies that the population mean for women
could be the same as
is less than
is greater than
the population mean for men.
d. State the assumptions upon which the interval in part c is based.
Upon which assumptions below is the interval based? Select all that apply.
A.The standard deviations of the two populations are approximately equal.
B.The population distribution for each group is approximately normal.
C.The samples from the two groups are independent.
D.The samples from the two groups are random.

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.

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.

asked 2021-02-09

A two-sample inference deals with dependent and independent inferences. In a two-sample hypothesis testing problem, underlying parameters of two different populations are compared. In a longitudinal (or follow-up) study, the same group of people is followed over time. Two samples are said to be paired when each data point in the first sample is matched and related to a unique data point in the second sample.

This problem demonstrates inference from two dependent (follow-up) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in sub-Saharan Africa. Conclusion about the null hypothesis is to note the difference between samples.

The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination. PSK\begin{array}{|c|c|} \hline Geographical\ regions & Before\ vaccination & After\ vaccination\\ \hline 1 & 85 & 11\\ \hline 2 & 77 & 5\\ \hline 3 & 110 & 14\\ \hline 4 & 65 & 12\\ \hline 5 & 81 & 10\\\hline 6 & 70 & 7\\ \hline 7 & 74 & 8\\ \hline 8 & 84 & 11\\ \hline 9 & 90 & 9\\ \hline 10 & 95 & 8\\ \hline \end{array}ZSK

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided \(\displaystyle{95}\%\) confidence interval for the true difference in population means. Test the null hypothesis that the population means are identical at the 0.05 level of significance.

This problem demonstrates inference from two dependent (follow-up) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in sub-Saharan Africa. Conclusion about the null hypothesis is to note the difference between samples.

The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination. PSK\begin{array}{|c|c|} \hline Geographical\ regions & Before\ vaccination & After\ vaccination\\ \hline 1 & 85 & 11\\ \hline 2 & 77 & 5\\ \hline 3 & 110 & 14\\ \hline 4 & 65 & 12\\ \hline 5 & 81 & 10\\\hline 6 & 70 & 7\\ \hline 7 & 74 & 8\\ \hline 8 & 84 & 11\\ \hline 9 & 90 & 9\\ \hline 10 & 95 & 8\\ \hline \end{array}ZSK

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided \(\displaystyle{95}\%\) confidence interval for the true difference in population means. Test the null hypothesis that the population means are identical at the 0.05 level of significance.

asked 2020-11-29

When we want to test a claim about two population means, most of the time we do not know the population standard deviations, and we assume they are not equal. When this is the case, which of the following is/are not true?

-The samples are dependent

-The two populations have to have uniform distributions

-Both samples are simple random samples

-Either the two sample sizes are large or both samples come from populations having normal distributions or both of these conditions satisfied.

-The samples are dependent

-The two populations have to have uniform distributions

-Both samples are simple random samples

-Either the two sample sizes are large or both samples come from populations having normal distributions or both of these conditions satisfied.

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.

asked 2021-01-19

Which of the following is not a condition for performing inference about a population mean U ?
A) Inference is based on n independent measurements.
B) The population distribution is Normal or the sample size is large (say n > 30).
C) The data are obtained from a SRS from the population of interest.
D) The population standard deviation, ? , must be known .

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.

asked 2020-12-28

Is statistical inference intuitive to babies? In other words, are babies able to generalize from sample to population? In this study,1 8-month-old infants watched someone draw a sample of five balls from an opaque box. Each sample consisted of four balls of one color (red or white) and one ball of the other color. After observing the sample, the side of the box was lifted so the infants could see all of the balls inside (the population). Some boxes had an “expected” population, with balls in the same color proportions as the sample, while other boxes had an “unexpected” population, with balls in the opposite color proportion from the sample. Babies looked at the unexpected populations for an average of 9.9 seconds (sd = 4.5 seconds) and the expected populations for an average of 7.5 seconds (sd = 4.2 seconds). The sample size in each group was 20, and you may assume the data in each group are reasonably normally distributed. Is this convincing evidence that babies look longer at the unexpected population, suggesting that they make inferences about the population from the sample?
Let group 1 and group 2 be the time spent looking at the unexpected and expected populations, respectively.
A) Calculate the relevant sample statistic.
Enter the exact answer.
Sample statistic: _____
B) Calculate the t-statistic.
Round your answer to two decimal places.
t-statistic = ___________
C) Find the p-value.
Round your answer to three decimal places.
p-value =

asked 2020-12-25

True // False: comparing means. Determine if the following statements are true or false, and explain your reasoning for statements you identify as false.

(a) When comparing means of two samples where \(n_{1} = 20\)

and \(n_{2} = 40\),

we can use the normal model for the difference in means since \(n_{2} \geq 30.\)

(b) As the degrees of freedom increases, the t-distribution approaches normality.

(c) We use a pooled standard error for calculating the standard error of the difference between means when sample sizes of groups are equal to each other.

(a) When comparing means of two samples where \(n_{1} = 20\)

and \(n_{2} = 40\),

we can use the normal model for the difference in means since \(n_{2} \geq 30.\)

(b) As the degrees of freedom increases, the t-distribution approaches normality.

(c) We use a pooled standard error for calculating the standard error of the difference between means when sample sizes of groups are equal to each other.

asked 2020-11-08

Give a ffull answer its true or false: When an ANOVA comparing the means of 3 groups indicates that at least one group is different from the others, a common follow-up analysis to determine which group(s) is (are) different is pairwise two-sample t-tests each assessed using
i) the pooled standard deviation when calculating the standard error for the difference in means and
ii) a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5%