Chapter 3: Tests Based on Sampling Distributions - II — Online MCQ Test
STATISTICS · CLASS 12th · Tamil Nadu State Board
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This chapter covers: This chapter covers F-test for equality of two variances chi-square test of goodness of fit and chi-square test of independence of attributes. Students master contingency table ana....
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Chapter 3: Tests Based on Sampling Distributions - II — Important Questions & Answers
In an F-test for equality of two population variances, the test statistic is based on the ratio of the two sample variances. Which form is usually taken?
- A. Smaller variance / Larger variance
- B. Larger variance / Smaller variance
- C. Sum of the two variances
- D. Difference of the two variances
Answer: B. Larger variance / Smaller variance
The F-statistic is generally formed as the ratio of the larger sample variance to the smaller sample variance so that the value is at least 1.
The F-statistic is generally formed as the ratio of the larger sample variance to the smaller sample variance so that the value is at least 1.
The chi-square test is commonly used to test whether the observed frequencies agree with the expected frequencies under a specified distribution. This is called the test of
- A. Independence of attributes
- B. Goodness of fit
- C. Equality of means
- D. Correlation
Answer: B. Goodness of fit
A chi-square goodness of fit test compares observed and expected frequencies to judge how well the data fit a given distribution.
A chi-square goodness of fit test compares observed and expected frequencies to judge how well the data fit a given distribution.
For a chi-square goodness of fit test, if the calculated value exceeds the table value at a given level of significance, then we
- A. accept the null hypothesis
- B. reject the null hypothesis
- C. accept the alternative hypothesis as true
- D. increase the degrees of freedom
Answer: B. reject the null hypothesis
If the calculated chi-square value is greater than the critical value, the deviation is significant and the null hypothesis is rejected.
If the calculated chi-square value is greater than the critical value, the deviation is significant and the null hypothesis is rejected.
Which of the following is the correct order of steps in a chi-square test of independence?
- A. Compute expected frequencies, form hypotheses, calculate chi-square, compare with table value
- B. Form hypotheses, compute expected frequencies, calculate chi-square, compare with table value
- C. Compare with table value, form hypotheses, calculate chi-square, compute expected frequencies
- D. Form hypotheses, compare with table value, compute expected frequencies, calculate chi-square
Answer: B. Form hypotheses, compute expected frequencies, calculate chi-square, compare with table value
The usual procedure is to set hypotheses first, then compute expected frequencies, calculate the chi-square statistic, and finally compare with the critical value.
The usual procedure is to set hypotheses first, then compute expected frequencies, calculate the chi-square statistic, and finally compare with the critical value.
Which of the following situations is best analyzed using the chi-square test of goodness of fit rather than the test of independence?
- A. Checking whether gender and blood group are related
- B. Checking whether two brands of machines have equal variances
- C. Checking whether a given set of observed frequencies follows a theoretical distribution
- D. Checking whether marks and height are correlated
Answer: C. Checking whether a given set of observed frequencies follows a theoretical distribution
Goodness of fit is used when observed frequencies are compared with a specified theoretical distribution, not to study association between two attributes.
Goodness of fit is used when observed frequencies are compared with a specified theoretical distribution, not to study association between two attributes.