Chapter Exam

Chapter 3: Tests Based on Sampling Distributions - II — Online MCQ Test

Q: 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?

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.

Q: 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

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.

Q: For a chi-square goodness of fit test, if the calculated value exceeds the table value at a given level of significance, then we

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.

STATISTICS · CLASS 12th · Tamil Nadu State Board

Practice Chapter 3: Tests Based on Sampling Distributions - II with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 12th STATISTICS. 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.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 3: Tests Based on Sampling Distributions - II — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 12th STATISTICS — Chapter 3: Tests Based on Sampling Distributions - II, with answers and explanations. These are sample questions; the exam has its own separate question set.

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 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.

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.

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.

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.