Question

A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if evaluations by students are related to salaries. To this end, he collected 100 observations on:y = Annual salary (in dollars)x = Mean score on teaching evaluationTo accomplish his goal, he assumes the following relationship:y = β(0) + β(1)x + ε Then, using Data Analysis, he obtained the following result.R2=0.23 Coefficient Standard Error Intercept 25675.5 11393x 5321 2119Required:What are the null and alternative hypotheses, respectively?

Answer 1

Complete Question

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Answer:

The null hypothesis is
`H_o : \beta_1 = 0`

The alternative hypothesis is
`H_1 : \beta_1 \\e 1`

Explanation:

From the question we are told that

The number observations is
`n = 100`

The annual salary (in dollars) is y

The mean score on teaching evaluation is x

The the relationship between the y and x is

`y = \beta_0 + \beta _1 x + \epsilon`

Where
`\beta _1` is the mean of the equation so

The null hypothesis is
`H_o : \beta_1 = 0`

The alternative hypothesis is
`H_1 : \beta_1 \\e 1`