In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither.
The population is normally distributed, and you know the population standard deviation.
I will use the normal distribution (z-distribution). When working with problems whose population is normally distributed and the population deviation, σ, is known, it is necessary to use the normal distribution.
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You don’t know the population standard deviation, and the sample size is 35.
I would use t distribution. When working with problems whose sample size is small and the standard deviation is not known, it is necessary to use t distribution.
The sample size is 22, and the population is normally distributed.
I would use t distribution. When working with problems whose population is normally distributed and the sample size is small, it is necessary to use a t distribution.
The sample size is 12, and the population is not normally distributed.
In this case, neither normal distribution nor t-distribution can be used. Normal distribution and t distribution cannot be used in this case since the population is not normally distributed.
The sample size is 45, and you know the population standard deviation.
I would use the normal distribution (z distribution). When working with problems whose sample size and the population standard deviation is known, it is necessary to use the normal distribution.
The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work.
From the problem, we are given the following;
And,
We are required to find the following;
Degrees of freedom
The degrees of freedom refers to the number of independent values that a statistical analysis can estimate. It is calculated by subtracting one from the sample size ( Bennet, Briggs, & Triola, 2018).
The critical value of t
From the t-distribution table, the critical value is 2.074.
The margin of error
The confidence interval for a 95% confidence level
For a confidence interval of 95%,
Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:
|
Play chess |
Don’t play chess |
|
| Male students |
25 |
162 |
| Female students |
19 |
148 |
Answer the following questions about the table. Be sure to show any calculations.
How many students in total were surveyed?
How many of the students surveyed play chess?
To determine the number of students who play chess from the survey, we need to add the number of male students who play and the number of female students who play chess.
What question about the population of students at the state college would this table attempt to answer?
The table is attempting to find the proportion of male students to female students who play chess at the state college.
State Hº and Hª for the test related to this table.
Let P 1 represent the number of male students who play chess, and P 2 represents the number of female students who play chess at the state college.
Answer the following questions about an ANOVA analysis involving three samples.
In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
An ANOVA analysis is a way of determining if survey results are significant (Kenton, 2019). In this ANOVA analysis, which involves three samples, we are attempting to compare the means of three samples and determine if there are any statistically significant differences between the means of these three samples. ANOVA’s F-statistic ration will be close to 1 if there are no significant differences between the three samples (Kenton, 2019).
State the null and alternate hypotheses for a three-sample ANOVA analysis.
What sample statistics must be known to conduct an ANOVA analysis?
Three sample statistics ought to be known in order to conduct an ANOVA analysis. These three sample statistics include; the sample size, the mean of the samples, and the standard deviation (Sullivan, N.d).
In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?
The F-statistic is a measure of variability among the means of the three samples. If the F test is lower than the critical value, it means that the means are not all equal. Thus, the null hypothesis ought to be rejected.
References
Bennet, J., Briggs, W., & Triola, M. (2018). Statistical reasoning for everyday life (5 th ed.). Boston, MA: Pearson Education.
Kenton, W. (2019). Analysis of variance (ANOVA). [Online]. Available at: https://www.investopedia.com/terms/a/anova.asp . Accessed 25 th May 2019.
Sullivan, L. (N.d). Hypothesis testing-Analysis of variance (ANOVA). [Online]. Available at: http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_HypothesisTesting-ANOVA/BS704_HypothesisTesting-Anova_print.html . Accessed 25 th May 2019.
