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

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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 for all your help in advance and hope that these answers are right!

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.

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

I cannot begin to imagine how you got your answer!

Thanks for all your help in advance and hope that these answers are right!

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