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# Hypothesis testing (P1 T2 320.2)

#### Taunk

##### Member
Hi,

320.2. Sixteen (16) financial institutions are surveyed. Their average overnight rate is 40.0 basis points with a sample standard deviation of 9.0 basis points. Which is nearest to the width of the two-sided 99.0% confidence interval (C.I.) for the "true" population mean overnight rate, where width of C.I. is upper limit minus lower limit.

Thanks

#### Dr. Jayanthi Sankaran

##### Well-Known Member
Hi @taunk,

In this problem, n = 16, sample standard deviation s(x) = 9 bps = 0.09%, and sample mean = 40 bps = 0.4%. We use the t-statistic to compute the CI for the "true" population mean (mu) overnight rate. CI = upper limit - lower limit

The CI is: Sample mean - critical t value (99%, 15)*s(x)/SQRT(n) <= mu(x) <= Sample mean + critical t value (99%, 15)*s(x)/SQRT(n)
Critical t-value for 1% significance with two-tails, 15 df: 2.947
Upper limit = 0.4% + 2.947*0.09%/SQRT(16) = 0.00466 = 0.466%
Lower limit = 0.4% - 2.947*0.09%/SQRT(16) = 0.00334 = 0.334%
Width of CI = Upper limit - Lower limit = 0.466% - 0.334% = 0.132% = 13.2 bps.

Hope that helps
Thanks!

#### Nicole Seaman

Staff member
Subscriber
Hello @taunk

Please make sure to use the links in the practice question sets that will bring you to the original forum post. This is where you will find the original forum link and discussion for this specific question: https://www.bionicturtle.com/forum/...dence-intervals-topic-review.7251/#post-26099. This helps to keep our forum organized, and many times you will find that your question has already been answered in the discussion.

Thank you

Nicole

#### Taunk

##### Member
Hi Nicole,
i appreciate your concern but whenever i click on the link to post in the link it says that i have insufficient privileges to reply to the post. Is it for every body or as per the package i have chosen. Please guide if possible.

Thanks

#### Nicole Seaman

Staff member
Subscriber
Hello @taunk

When this happens, it indicates that your forum permissions need to be reset. You should always have full forum access as long as you have purchased one of our packages. Now that I have reset your permissions, you will need to clear your cache and cookies. You should have full forum access now. If this happens again in the future, please let me know so I can fix it.

Thank you,

Nicole

#### Taunk

##### Member
Hi Nicole,

Now i can post. Thank you. I had a lot of doubts which i did not post lest i will have to go through the whole process of starting a new thread.

Thank you,