1. ## Statistics help...

We were give a lot of problems in our probability and statistics lecture, and i am currently in need of URGENT help...

I am currently working on this problems, and i believe i can solve some problems here, but in any case, i would still post all the problems just to also be an assurance of my answer.

1. A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the difference of the calories is approximately normal.

2. Students may choose between a 3-semester- hour course in physics without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. If 12 students in the section with labs made an average examination grade of 84 with standard deviation of 4, and 18 students in the section without labs made an average grade of 77 with a standard deviation of 6, find a 99% interval for the difference between the average grades for the two courses. Assume the populations to be approximately normally distributed with equal variances.

3. Ten engineering schools in the US were surveyed. The sample contained 250 electrical engineers, 80 being women; 175 chemical engineers, 40 being women. Compute a 90% confidence interval for the difference between the proportion of women in these fields of engineering. Is there a significant difference between the two proportions?

4. According to a dietary study a high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single servings of ready-to-eat cereals. If a random sample of 20 similar servings of Special K has a mean sodium content of 24.5 milligrams, does this suggest that the 0.05 level of significance that the average sodium content for single servings of Special K is greater than 220 milligrams? Assume the distribution of sodium contents to be normal.

5. A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms. To test his claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread had an average tensile strength of 86.7 kilograms with a standard deviation of 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms with a standard deviation of 5.61 kilograms. Test the manufacturer's claim using a 0.05 level of signifcance.

6. A dice is tossed 180 times with the following results

x | 1 | 2 | 3 | 4 | 5 | 6 |
--+---+---+---+---+---+---+
f | 28 | 36| 36| 30 | 27| 23 |

Is this a balanced dice? Use a 0.01 level of significance.

2. Originally Posted by asteg123
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1. A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the difference of the calories is approximately normal.
The random variable:

$\displaystyle t=\frac{\bar{x}-\mu}{s/\sqrt{N}}$

where $\displaystyle \bar{x}$ is the sample mean, $\displaystyle \mu$ is the population mean, $\displaystyle s$ is the sample SD, and $\displaystyle N$ is the sample size, has a t-distribution with $\displaystyle N-1$ degrees of freedom.

Now we look up the size of a 99% interval for a t-distributed random variable with $\displaystyle 9$ degrees of freedom, this is $\displaystyle (-3.25, 3.25)$, so with a bit of manipulation we have the 99% interval for $\displaystyle \mu$ is:

$\displaystyle \left(\bar{x}-3.25\ s/\sqrt{10} ,\ \bar{x}+3.25\ s/\sqrt{10}\right)\approx (214.58, 245.42)$

RonL

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### a manufacturer claims that the average tensile strength

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