Question set 1 Z-test null and alternate hypothesis set up ? Conclusion? T-test null and alternate hypothesis set up ? Conclusion ? Question set 2

QUESTION

Question set 1

Z-test null and alternate hypothesis set up ?

Conclusion?

T-test null and alternate hypothesis set up ?

Conclusion ?

Question set 2

1. Run a one-way ANOVA to compare three or more groups of people (specified by a categorical variable) on one continuous variable.
   1. Write the null and alternate hypotheses.
   2. What is the calculated mean for each group?
   3. What is the calculated F value?
   4. What is the p and critical F value?
   5. Is the p value significant? Is calculated F value greater than Critical F value? Conclusion?
2. Run a chi-squared test to determine whether one group of people has higher rates of a given outcome relative to the other groups of people in the data set.
   1. Write the null and alternate hypotheses.
   2. What is the calculated chi-square value?
   3. What is the p and critical value?
   4. Is the p value significant? Is calculated chi-square value greater than Critical F value? Conclusion?

ANSWER

Question set 1

Z-test null and alternate hypothesis setup

The null hypothesis (H0) for a Z-test states that there is no significant difference between a sample mean and a population mean. The alternate hypothesis (Ha) states that there is a significant difference between the sample mean and the population mean.

Conclusion

To draw a conclusion in a Z-test, we compare the calculated Z-value with the critical Z-value corresponding to the desired level of significance. If the calculated Z-value falls within the critical region (beyond the critical Z-value), we reject the null hypothesis and conclude that there is a significant difference between the sample mean and the population mean. If the calculated Z-value does not fall within the critical region, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant difference.

T-test null and alternate hypothesis setup

The null hypothesis (H0) for a T-test states that there is no significant difference between the means of two populations or between a sample mean and a known population mean. The alternate hypothesis (Ha) states that there is a significant difference between the means.

Conclusion

To draw a conclusion in a T-test, we compare the calculated T-value with the critical T-value corresponding to the desired level of significance. If the calculated T-value falls within the critical region (beyond the critical T-value), we reject the null hypothesis and conclude that there is a significant difference between the means. If the calculated T-value does not fall within the critical region, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant difference.

Question set 2

One-way ANOVA null and alternate hypotheses setup

The null hypothesis (H0) for a one-way ANOVA states that there is no significant difference in the means of the groups being compared. The alternate hypothesis (Ha) states that there is a significant difference in the means of the groups.

Calculated mean for each group

The calculated mean for each group is the average value of the continuous variable within that group.

Calculated F-value

The calculated F-value is obtained from the ANOVA test and measures the ratio of between-group variability to within-group variability.

P-value and critical F-value

The p-value represents the probability of obtaining the observed F-value or a more extreme value under the assumption that the null hypothesis is true. The critical F-value is the F-value corresponding to the desired level of significance.

Significance of p-value and calculated F-value

If the p-value is lower than the chosen significance level (e.g., 0.05), we reject the null hypothesis and conclude that there is a significant difference between at least one pair of groups. Additionally, if the calculated F-value is greater than the critical F-value, we reject the null hypothesis.

Conclusion

Based on the analysis, if the p-value is significant (lower than the chosen significance level) and the calculated F-value is greater than the critical F-value, we can conclude that there is sufficient evidence to suggest a significant difference in means between the groups.

Chi-squared test null and alternate hypotheses setup

The null hypothesis (H0) for a chi-squared test states that there is no association between the categorical variable and the given outcome in the groups being compared. The alternate hypothesis (Ha) states that there is an association between the categorical variable and the given outcome.

Calculated chi-square value

The calculated chi-square value is obtained from the chi-squared test and measures the degree of association between the categorical variable and the given outcome.

P-value and critical value

The p-value represents the probability of obtaining the observed chi-square value or a more extreme value under the assumption that the null hypothesis is true. The critical value is the chi-square value corresponding to the desired level of significance.

Significance of p-value and calculated chi-square value

If the p-value is lower than the chosen significance level (e.g., 0.05), we reject the null hypothesis and conclude that there is a significant association between the categorical variable and the given outcome. Additionally, if the calculated chi-square value is greater than the critical value, we reject the null hypothesis.

Conclusion

Based on the analysis, if the p-value is significant (lower than the chosen significance level) and the calculated chi-square value is greater than the critical value, we can conclude that there is sufficient evidence to suggest a significant difference in rates of the given outcome among the groups.