in an effort to increase production of an automobile part, the factory manager decides to play music in the manufacturing area. Eight workers are selected, and the number if items each produced for a specfic day is recored. After one week of music, the same workers are monitored again. The data are given in the table. AT x=0.05, can the manager conclude that the music has increase prodcution?

awdawd

To determine whether the music has increased production, we need to perform a hypothesis test. In this case, we will be conducting a paired t-test because we are comparing the results of the same workers before and after the implementation of the music.

Here is the step-by-step explanation on how to perform the test:

Step 1: State the null and alternative hypothesis:
- Null hypothesis (H0): The music has no effect on production. The mean difference in production before and after music is zero.
- Alternative hypothesis (Ha): The music has increased production. The mean difference in production before and after music is greater than zero.

Step 2: Select a significance level (alpha):
The significance level, denoted as alpha (α), determines the threshold for accepting or rejecting the null hypothesis. In this case, the significance level is given as x=0.05.

Step 3: Calculate the test statistic:
First, calculate the difference in production for each worker between the before and after music period. Then calculate the mean and standard deviation of these differences.

Step 4: Calculate the t-statistic:
Using the formula: t = (mean difference - hypothesized mean) / (standard deviation / sqrt(n))

Step 5: Determine the critical value or p-value:
We will use the t-distribution to find the critical value based on the degrees of freedom (df = n-1). Compare the calculated t-statistic with the critical value to make a decision. Alternatively, you can calculate the p-value associated with the t-statistic.

Step 6: Make a decision:
If the calculated t-statistic is greater than the critical value or if the p-value is less than the significance level (α), reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Note: The critical value can be found using a t-table or statistical software, and the p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

So, with this process, you can determine whether the music has increased production based on the given data and the significance level.