A teacher claims that, on average, 30% of students in his class get an A, 15% get a B, 15% get a C, 40% get a D and the rest get an F. The grades of a random sample of his students over the years is recorded. Test the claim at 0.05% significance. Test for the claim that the following categories occur with the following frequencies: pA=0.3pA=0.3; pB=0.15pB=0.15; pC=0.15pC=0.15; pD=0.4pD=0.4Test at the 0.05 significance level. Complete the table. Round all answers to three decimal places. Category Observed Frequency Expected Frequency Residual A 17 B 14 C 32 D 40 HoHo : pA=0.3pA=0.3; pB=0.15pB=0.15; pC=0.15pC=0.15; pD=0.4pD=0.4 H1H1: at least one is different Original claim = Select an answer H₁ H₀ Enter the critical value, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.) X2Χ2(,) = (Round to three decimal places.) Test Statistic = (Round to three decimal places.) p-value= (Round to four decimal places.) Decision: Select an answer Accept the null hypothesis Reject the null hypothesis Accept the alternative hypothesis Fail to reject the null hypothesis Conclusion: Select an answer The sample data supports There is not enough evidence to support There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of the claim that all 4 categories are equally likely to be selected. Submit QuestionQuestion 2
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A teacher claims that, on average, 30% of students in his class get an A, 15% get a B, 15% get a C, 40% get a D and the rest get an F. The grades of a random sample of his students over the years is recorded. Test the claim at 0.05% significance.
Test for the claim that the following categories occur with the following frequencies:
| Category | Observed Frequency |
Expected Frequency |
Residual |
|---|---|---|---|
| A | 17 | ||
| B | 14 | ||
| C | 32 | ||
| D | 40 |
HoHo : pA=0.3pA=0.3; pB=0.15pB=0.15; pC=0.15pC=0.15; pD=0.4pD=0.4
H1H1: at least one is different
Original claim = Select an answer H₁ H₀
Enter the critical value, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.)
(Round to three decimal places.)
Test Statistic = (Round to three decimal places.)
p-value=
(Round to four decimal places.)
Decision: Select an answer Accept the null hypothesis Reject the null hypothesis Accept the alternative hypothesis Fail to reject the null hypothesis
Conclusion: Select an answer The sample data supports There is not enough evidence to support There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of the claim that all 4 categories are equally likely to be selected.
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