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In cases where you have an existing historical claim or assumption, the null hypothesis often states that it is true. In such cases, the alternative hypothesis challenges the historical claim in an attempt to disprove the same. The following are a few important points to be kept in mind while framing null and alternative hypotheses:The null and alternative hypotheses are perfect opposites of each other. Hence, they should cover the entire range of possibilities that the hypothesised parameter can take.The null hypothesis always has the following signs: ‘=’, ‘≤’ or ‘≥’.The alternative hypothesis always has the following signs: ‘≠’, ‘>’ or ‘<’.In the next video, our faculty, Rahim will walk you through some examples of framing null and alternative hypotheses in different contexts.Question 2/2MandatoryThe Null and Alternative HypothesesWhich of the following can function as a pair of hypotheses?Ho: Average age of employees = 28 years; Ha: Average age of employees < 28 yearsHo: Average age of employees ≠ 33 years; Ha: Average age of employees = 33 yearsHo: Average age of employees ≥ 32 years; Ha: Average age of employees < 27 yearsHo: Average age of employees ≤ 41 years; Ha: Average age of employees > 41 years

Question

In cases where you have an existing historical claim or assumption, the null hypothesis often states that it is true. In such cases, the alternative hypothesis challenges the historical claim in an attempt to disprove the same. The following are a few important points to be kept in mind while framing null and alternative hypotheses:The null and alternative hypotheses are perfect opposites of each other. Hence, they should cover the entire range of possibilities that the hypothesised parameter can take.The null hypothesis always has the following signs: ‘=’, ‘≤’ or ‘≥’.The alternative hypothesis always has the following signs: ‘≠’, ‘>’ or ‘<’.In the next video, our faculty, Rahim will walk you through some examples of framing null and alternative hypotheses in different contexts.Question 2/2MandatoryThe Null and Alternative HypothesesWhich of the following can function as a pair of hypotheses?Ho: Average age of employees = 28 years; Ha: Average age of employees < 28 yearsHo: Average age of employees ≠ 33 years; Ha: Average age of employees = 33 yearsHo: Average age of employees ≥ 32 years; Ha: Average age of employees < 27 yearsHo: Average age of employees ≤ 41 years; Ha: Average age of employees > 41 years

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Solution

The correct pair of hypotheses from the options given is:

Ho: Average age of employees ≤ 41 years; Ha: Average age of employees > 41 years

This is because the null hypothesis (Ho) and the alternative hypothesis (Ha) are perfect opposites of each other. The null hypothesis states that the average age of employees is less than or equal to 41 years, while the alternative hypothesis states that the average age of employees is greater than 41 years. This covers the entire range of possibilities that the hypothesized parameter (average age of employees) can take.

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