# Getting better - but still need to check my answers!!

• April 1st 2008, 04:36 PM
darren_a1
Getting better - but still need to check my answers!!
Hi guys!!:

I am getting better at Stat - i still hate it though! I had a whole bunch of q's to do today and i did every single one of them! I was hoping that some1 could please help me check and make sure that my answers are correct! for ease of understanding I put the answers that i got in BOLD and a different color!

1. Of 139 adults selected randomly from one town, 30 of them smoke.
The main concern I have on this question is we take (30/139) = .215 or 21.5% ... now do we keep that as is or do we round it off to 22% ?

a. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke. 12.6%<p<30.4%
b. Construct a 95% confidence interval for the true percentage of all adults in the town that smoke. 14.7%<p<28.3%

2. The speeds (in mph) of the cars passing a certain checkpoint are measured by radar. The results for a random sample are shown below.

44.4 41.8 42.9 40.7 43.5 40.1 44.6 41.9
44.4 42.0 43.5 41.9 40.7 43.5 41.8

a. Find x-bar and s for this data set. x-bar = 42.513 s = 1.439
b. Construct a 90 percent confidence interval for the mean speed of cars passing this checkpoint. You may assume the speeds are normally distributed. 41.9<-->43.1241

3.A random sample of the duration of 50 telephone calls handled by a local telephone company had a mean of 11.6 min and a standard deviation of 3.8 minutes. Find a 95% confidence interval for the true mean duration of calls handled by the company. [10-55 - 12.65]

4. A parcel service selected a random sample of 17 packages in order to estimate the mean weight of all packages received by the service. The sample had a mean weight of 15.3 pounds and a standard deviation of 1.9 pounds. Find the 95% confidence interval for the true mean weight of all packages received by the parcel service. You may assume package weights are normally distributed. [6.27 - 24.33] --> this range seemed to high to me! any ideas or thoughts?

Thanks all
• April 2nd 2008, 04:50 AM
mr fantastic
Quote:

Originally Posted by darren_a1
Hi guys!!:

I am getting better at Stat - i still hate it though! I had a whole bunch of q's to do today and i did every single one of them! I was hoping that some1 could please help me check and make sure that my answers are correct! for ease of understanding I put the answers that i got in BOLD and a different color!

1. Of 139 adults selected randomly from one town, 30 of them smoke.
The main concern I have on this question is we take (30/139) = .215 or 21.5% ... now do we keep that as is or do we round it off to 22% ?

Mr F says: Use 0.216.

a. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke. 12.6%<p<30.4%

Mr F says: ${\color{blue} 0.216 - 2.58 \sqrt{\frac{(0.216) (0.785)}{139}} < p < 0.216 + 2.58 \sqrt{\frac{(0.216) (0.785)}{139}}}$ ${\color{blue} \Rightarrow 0.126 < p < 0.306 \Rightarrow 12.6 \% < p < 30.6 \%}$.

b. Construct a 95% confidence interval for the true percentage of all adults in the town that smoke. 14.7%<p<28.3%

Mr F says: ${\color{blue} 0.216 - 1.96 \sqrt{\frac{(0.216) (0.785)}{139}} < p < 0.216 + 1.96 \sqrt{\frac{(0.216) (0.785)}{139}}}$ ${\color{blue} \Rightarrow 0.148 < p < 0.284 \Rightarrow 14.8 \% < p < 28.4 \%}$.

2. The speeds (in mph) of the cars passing a certain checkpoint are measured by radar. The results for a random sample are shown below.

44.4 41.8 42.9 40.7 43.5 40.1 44.6 41.9
44.4 42.0 43.5 41.9 40.7 43.5 41.8

a. Find x-bar and s for this data set. x-bar = 42.513 s = 1.439
b. Construct a 90 percent confidence interval for the mean speed of cars passing this checkpoint. You may assume the speeds are normally distributed. 41.9<-->43.1241

Mr F says: Use the t-statistic here (15 - 1 = 14 degrees of freedom) because population standard deviation is unknown and n = 15 is small. The critical value is t = 1.345.

${\color{blue} 42.513 - 1.345 \frac{1.439}{\sqrt{15}} < \mu < 42.513 + 1.345 \frac{1.439}{\sqrt{15}} \Rightarrow 42.01 < \mu < 43.01}$.

3.A random sample of the duration of 50 telephone calls handled by a local telephone company had a mean of 11.6 min and a standard deviation of 3.8 minutes. Find a 95% confidence interval for the true mean duration of calls handled by the company. [10-55 - 12.65]

Mr F says: Use the z-statistic here because athough population standard deviation is unknown, n = 50 is large. The critical value is z = 1.96.

${\color{blue} 11.6 - 1.96 \frac{3.8}{\sqrt{50}} < \mu < 11.6 + 1.96 \frac{3.8}{\sqrt{50}} \Rightarrow 10.55 < \mu < 12.65}$.

4. A parcel service selected a random sample of 17 packages in order to estimate the mean weight of all packages received by the service. The sample had a mean weight of 15.3 pounds and a standard deviation of 1.9 pounds. Find the 95% confidence interval for the true mean weight of all packages received by the parcel service. You may assume package weights are normally distributed. [6.27 - 24.33] --> this range seemed to high to me! any ideas or thoughts?

Mr F says: Use the t-statistic here (17 - 1 = 16 degrees of freedom) because population standard deviation is unknown and n = 17 is small. The critical value is t = 1.746.

${\color{blue} 15.3 - 1.746 \frac{1.9}{\sqrt{17}} < \mu < 15.3 + 1.746 \frac{1.9}{\sqrt{17}} \Rightarrow 14.50 < \mu < 16.10}$.

Thanks all

..
• April 2nd 2008, 07:06 AM
darren_a1
got it!
Mr Fantastic!

Thanks for your reply. I understood and learnt where i made my mistakes. except on the last one..
Quote:

Mr F says: Use the t-statistic here (17 - 1 = 16 degrees of freedom) because population standard deviation is unknown and n = 17 is small. The critical value is t = 1.746.
How do you get the critical value t ?? I used the table too, but i got 2.110 by looking under the area in two tails! Also the same with question #2 , shouldnt we be looking under Area in Two Tails, as the book says 95% confidence level corresponds to alpha = 0.05, which is divided equally between two tails!

hope to get that cleared up in my head!

Thanks

Darren
• April 2nd 2008, 01:13 PM
mr fantastic
Quote:

Originally Posted by darren_a1
Mr Fantastic!

Thanks for your reply. I understood and learnt where i made my mistakes. except on the last one..

How do you get the critical value t ?? I used the table too, but i got 2.110 by looking under the area in two tails! Also the same with question #2 , shouldnt we be looking under Area in Two Tails, as the book says 95% confidence level corresponds to alpha = 0.05, which is divided equally between two tails!

hope to get that cleared up in my head!

Thanks

Darren

Quite right - my mistake (it was late is my excuse). I accidently used a single tail.
• April 2nd 2008, 04:45 PM
darren_a1
thanks much!
Mr fantastic:

Thanks for the update!

Looks like am almost done with these. I have one more Q - similar to these. I will post it on here under a new topic once am done! I just need help to double check the answer as usual!

THanks

Darren