FA SEM III Minor July 2025

At the Bright Minds Coaching Center, Eshaan, Aanya, and Aarav are eager to find out if their new teaching method has worked wonders this year! Last year, the average score was 75 marks, but this year, they gathered a sample of 50 students who scored an average of 77 with a standard deviation of 10. Can you help them figure out the alternative hypothesis?

• H1: The average score this year is less than 75 marks.

• H1: The average score this year is greater than 75 marks.

• H1: The average score this year is less than or equal to 75 marks.

• H1: The average score this year is equal to 75 marks.

At the Bright Minds Coaching Center, our beloved students Saisha, Avyaan, and Aisha are eager to find out if their new teaching method has truly made a difference! Last year, the average score was 75 marks, but this year, after applying their innovative techniques, a sample of 50 students scored an average of 77 with a standard deviation of 10. Now, the big question is: should we conduct a one-tailed test or a two-tailed test to see if the scores have improved?

• Three-tailed test with a different hypothesis

• One-tailed test

• Two-tailed test

• No test needed

At the Bright Minds Coaching Center, Aanya, Sanya, and Avani are eager to find out if their new teaching method has worked wonders! Last year, the average score was 75 marks, but this year, they gathered a sample of 50 students who scored an average of 77 with a standard deviation of 10. Can you help them choose the right statistical test to examine the null hypothesis and see if their method really made a difference?

• One-sample t-test

• Chi-square test

• ANOVA

• Two Sample t-test

At the Bright Minds Coaching Center, our enthusiastic students, including Aisha, Akhil, and Tara, are eager to find out if their new teaching method has truly made a difference! Last year, the average score was 75 marks, but this year, after a lot of hard work, a sample of 50 students scored an average of 77 with a standard deviation of 10. Can you help us determine the sampling distribution of the test statistic to test the null hypothesis?

• Chi-square distribution

• Z-distribution

• F-distribution

• Student’s t-distribution with n−1 df

At the Bright Minds Coaching Center, our beloved students Aanya, Vanya, and Eesha are eager to find out if their new teaching method has worked wonders! Last year, the average score was 75 marks, but this year, after a lot of hard work, a sample of 50 students scored an average of 77 with a standard deviation of 10. With a p-value of 0.08, what exciting decision can we make about their scores?

• Fail to reject the null hypothesis; no significant improvement in scores.

• Reject the null hypothesis; significant improvement in scores.

• Accept the null hypothesis; scores decreased significantly.

• Reject the null hypothesis; scores are exactly the same as last year.

At the Bright Minds Coaching Center, Riyaan, Aditi, and Tara are eager to find out if their exciting new teaching method has helped improve their scores compared to last year’s average of 75 marks. This year, they gathered a sample of 50 students who scored an average of 77 with a standard deviation of 10. If the p-value is 0.08, what fun conclusion can they draw about their new method?

• The new method improved scores significantly!

• We don’t have enough evidence to say the new method improved scores.

• Scores have worsened.

• Students scored the same as before.

A factory claims at most 5% of their products are defective. One day, Aisha, a quality inspector, decides to put this claim to the test. She carefully inspects 200 items and discovers 15 defective ones. Now, Aisha is curious about the alternative hypothesis. What could it be?

• The alternative hypothesis is that exactly 5% of the products are defective.

• The alternative hypothesis is that less than 5% of the products are defective.

• The alternative hypothesis is that no products are defective.

• The alternative hypothesis is that more than 5% of the products are defective.

In a bustling factory, Aanya is on a mission to ensure quality control! The factory boldly claims that at most 5% of their products are defective. With her trusty clipboard, Aanya tests 200 items and discovers a surprising 15 defective products. Now, the big question is: should Aanya conduct a one-tailed or two-tailed test to verify the factory's claim?

• Two-tailed

• One-tailed (right)

• One-tailed (left)

• Not applicable

In a bustling factory, our friend Shaan is on a mission to ensure quality! The factory boldly claims that at most 5% of their products are defective. So, Shaan, armed with his trusty clipboard, tests 200 items and discovers a shocking 15 defective items. Now, the big question is: which statistical test should Shaan choose to challenge the factory's claim and test the null hypothesis?

• Two-sample t-test

• Chi-square test

• ANOVA test

• One-sample proportion test

In a bustling factory, our friend Aashi is on a mission to ensure quality! The factory boldly claims that at most 5% of their products are defective. Aashi, the diligent quality inspector, tests 200 items and discovers 15 defective ones. Can you help Aashi figure out the sampling distribution of the test statistic?

• Z distribution

• t-distribution

• F distribution

• Chi-square distribution