P1.T2.320. Statistical inference: hypothesis testing and confidence intervals

[Nicole Seaman]

Questions:

320.1. Recently 25 banks were surveyed. Their sample average total capital is 8.40% (i.e., Tier 1 plus Tier 2 as a percentage of risk-weighted assets, RWA) with a sample standard deviation of 1.0%. Our one-sided null hypothesis is that the population's "true" average total capital is less than or equal to 8.0%. With 95.0% confidence, can we accept the one-sided alternative hypothesis that the population's average total capital is greater than 8.0%?

a. No, we do not accept the alternative because our computed test statistic of 2.797 is greater than the critical (lookup) t value of 2.000
b. No, we do not accept the alternative because our computed test statistic of 2.000 is less than the critical (lookup) t value of 2.064
c. Yes, we accept the alternative because our computed test statistic of 2.000 is greater than the critical (lookup) t value of 1.711
d. Yes, we accept the alternative because our computed test statistic of 1.318 is less than the critical (lookup) t value of 2.492

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?

a. 4.75 bps
b. 9.59 bps
c. 13.26 bps
d. 24.07 bps

320.3. A random sample of 18 daily returns generated by a low-volatility exchange-traded fund (ETFs) produces a sample daily volatility of 10 basis points. What is the two-sided 95.0% confidence interval for the fund's true (population) daily return volatility?

a. 4.0 to 16.0
b. 7.0 to 13.0
c. 7.5 to 15.0
d. 8.5 to 16.3

Answers:

• Here in forum

 

[prebhan27]

I have a question to 302.2.: How do we know to use the t-statistic here for the lookup value instead of the z-statistic in order to create the C.I.?
Thanks in advance!

 

[ShaktiRathore]

Hi there are two cases possible:
1)population std deviation is given:Whenever sample size(# observations)<30 use t stat look up. For size>=30 its safe to use z stat.
2)population std deviation is not given but sample std deviation is given as in above examples:sample size <30 use t stat/look up .For size>=30 use t stat look up but it becomes more safer to use zstat as size increases however its still more safer/better to use t stat.as size increases the distinctiin b/w t and z blurrs so in end either z or t would work at larger sizes.still i shall go with t stat.
Thanks

 

[prebhan27]

Thanks a lot !