Question

Fidelity Investments is a Boston institution that is “among the most diversified financial services companies in the world, offering a full range of product solutions for individual investors, employers, institutions, and intermediaries. Fidelity has $6.8 billion in assets under administration, including managed assets of $2.4 billion, as of December 31, 2018”
Fidelity operates service centers in various cities that customers can call to get answers to questions about their investments. Previously, the company studied the distribution of time required for each call. It found that calls are normally distributed, with a mean equal to 540 seconds. The call center manager in Provo, Utah, has selected a random sample of 50 calls and wants to determine whether the mean call time is now less than 540 seconds after a training program given to call center employees. She can test whether the time has decreased by using the following steps:

1. Set up a hypothesis
2. Set up a suitable significance level
3. Determine a suitable test statistic
4. Determine the critical region
5. Perform computations
6. Make decision to accept or reject hypothesis
   1. Make decision to accept or reject hypothesis

PLEASE HELP, SET UP ANY HYPOTHESIS. THANKS

Answer 1

Let be the mean call time (population paramater) now (ie after training program

a)

Hypotheses

b) Significance level = 0.05

c)

We can't calculate anything as sample standard deviation and means are not given. I am providing the formula to be used

Test statistic

d)

Its a left tail test. And critical value for n =50 and alpha = 0.05 is -1.677

Rejection region is R=t: t<−1.677

e)

If t-stat is less than tc, we reject the null hypothesis

Please let me know if you have any doubts. Happy to help. Please thumbs up if you like the solution. Thanks