Question

A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. The professional employees should volunteer an average of more than 15 hours per month. A random sample of 24 professional employees reported the following number of hours per month: 12 13 14 14 15 15 15 16 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 21 Test significance level at 5% that the professional employees will be volunteer an average of more than 15 hours per month in engaging during local service activities. (a) Write the null (H0) and alternative (H1) hypothesis. (b) State the critical value of the above hypothesis testing. (c) Calculate the test statistic. (d) Shall we reject the null (H0) hypothesis of these professional employees’ monthly hours in volunteering during local service activities?

          A large software development firm recently relocated its facilities. Top management is
interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. The
professional employees should volunteer an average of more than 15 hours per month.
A random sample of 24 professional employees reported the following number of hours
per month:

12 13 14 14 15 15 15 16
16 16 16 16 17 17 17 18
18 18 18 19 19 19 20 21

Test significance level at 5% that the professional employees will be volunteer an
average of more than 15 hours per month in engaging during local service activities.
(a) Write the null (H0) and alternative (H1) hypothesis.
(b) State the critical value of the above hypothesis testing.
(c) Calculate the test statistic.
(d) Shall we reject the null (H0) hypothesis of these professional employees’ monthly
hours in volunteering during local service activities?

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Added by Jingwen L.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Samriddhi Singh

04/08/2023

Step 1

H0: μ = 15 (The average number of volunteer hours per month is 15) H1: μ > 15 (The average number of volunteer hours per month is greater than 15) (b) State the critical value of the above hypothesis testing. Since the significance level is 5% (0.05) and this Show more…

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A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. The professional employees should volunteer an average of more than 15 hours per month. A random sample of 24 professional employees reported the following number of hours per month: 12 13 14 14 15 15 15 16 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 21 Test significance level at 5% that the professional employees will be volunteer an average of more than 15 hours per month in engaging during local service activities. (a) Write the null (H0) and alternative (H1) hypothesis. (b) State the critical value of the above hypothesis testing. (c) Calculate the test statistic. (d) Shall we reject the null (H0) hypothesis of these professional employees’ monthly hours in volunteering during local service activities?

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Transcript

00:01 Hello everyone.

00:03 So in this question for given 24 random sample data points of professional employees, we have to find the null and alternative hypothesis, the t -critical value, test critical value.

00:23 Further, we have to find the test statistics and then find the conclusion.

00:29 So as per the given information, the xi values are given where xi is the value of hours per month of various employees where the values of i range from 1 to 24.

01:01 The total n that is 24 employees data given.

01:07 So first we find the value of summation xi that is sum of all the 24 data points which will be equals to 399.

01:18 Now we calculate mean and standard deviation.

01:21 So mean which is x bar will be equals to summation xi divided by n.

01:30 So substituting the values here, we have summation xi is 399 divided by n which is 24 which will be equals to 16 .625 approximately.

01:43 Talking about standard deviation, standard deviation s is equals to square root summation xi minus x bar whole square divided by n minus 1 summation over i where the values of i range from 1 to 24.

02:07 Now substituting all the values, we have the value of x bar and in the question we have 24 values of xi, i from 1 to 24.

02:15 So this becomes square root summation xi minus x bar whole square will be approximately 113 .625 divided by n minus 1 that is 23 which in solving is approximately equals to 2 .2227.

02:41 Now coming to part a of the question, we have to state null and alternative hypothesis.

02:49 So professional employees will be volunteer on average of more than 15 hours per month in engaging during local service activities.

02:59 So the null hypothesis becomes h0 such that mu is less than equals to 15 which is tested against the alternative hypothesis ha such that mu is greater than 15...

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