Write the null and alternative hypotheses in words and then symbols for each of the following situations. a. A tutoring company would like to understand if most students tend to improve their grades (or not) after they use their services. They sample 200 of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year.
b. Employers at a firm are worried about the effect of March Madness, a basketball championship held each spring in the US, on employee productivity. They estimate that on a regular business day employees spend on average 15 minutes of company time checking personal email, making personal phone calls, etc. They also collect data on how much company time employees spend on such non-business activities during March Madness. They want to determine if these data provide convincing evidence that employee productivity changed during March Madness.

The Null hypothesis is the initial truth which we would like to counter using the alternative hypothesis. The Null and Alternative hypothesis for the given situation are :

1.)

Null hypothesis : There have been no change in the grade obtained by the students.

Alternative hypothesis : The grade obtained by the students have improved as students now attain better grades after attending the tutoring class

Using symbol :

2.)

Null hypothesis : There is no change in the productivity of employees during the period as the amount of time spent on non-business activities remains the same.

Alternative hypothesis : There is a change in productivity has employees spend more than 15 minutes engaging on non-business activities.

Using symbol :

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A) the hypothesis in words and symbols are;

Null hypothesis: Grades have not improved for most students

Alternative hypothesis: Grades have improved for most students

Null hypothesis; H0: p^ = 0.5

Alternative hypothesis; Ha: p^ > 0.5

B) Null hypothesis: During march madness, employees averaged 15 minutes per day on non - business activities

Alternative hypothesis: During march madness, employees averaged more than 15 minutes per day on non-business activities

Null hypothesis; H0: μ = 15

Alternative hypothesis; Ha: μ > 15

Step-by-step explanation:

A) We are told that they sampled 200 of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year. Thus, there will be a 50% chance of success for their grades to have improved and a 50% chance for it to remain the same.

Thus; p^ = 0.5

So the hypothesis in words and symbols are;

Null hypothesis: Grades have not improved for most students

Alternative hypothesis: Grades have improved for most students

Null hypothesis; H0: p = 0.5

Alternative hypothesis; Ha: p > 0.5

B) We are told that they estimate that on a regular business day employees spend on average 15 minutes of company time checking personal email, making personal phone calls, etc

Also, They also collect data on how much company time employees spend on such non-business activities during March Madness.

The hypotheses in words and symbols are;

Null hypothesis: During march madness, employees averaged 15 minutes per day on non - business activities

Alternative hypothesis: During march madness, employees averaged more than 15 minutes per day on non-business activities

Null hypothesis; H0: μ = 15

Alternative hypothesis; Ha: μ > 15

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,