# Multiple choice: Normal distribution, Confidence Interval

1. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with m = 110 grams and Q(standard deviation)= 25 grams. A sample of 25 vitamins is to be selected. So, the middle 70% of all sample means will fall between what two values?

a) 104.8 and 115.2

b) 108.4 and 112.5

c) 115 and 100.7

d) 85 and 125

2. Which of the following about the normal distribution is not true?

a) Theoretically, the mean, median, and mode are the same.

b) About 2/3 of the observations fall within +,-1 standard deviation from the mean.

c) It is a discrete probability distribution.

d) Its parameters are the mean, m, and standard deviation, Q .

3. A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall.

Fifteen credit card accounts were randomly sampled and analyzed with the following results: X(sample mean)=$50.50 and S square=400. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall.

a) $50.50+,- $9.09

b) $50.50+,- $10.12

c) $50.50+,- $11.00

d) $50.50+,- $11.08

I need detail explanation

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#### Solution Preview

1. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with m = 110 grams and Q(standard deviation)= 25 grams. A sample of 25 vitamins is to be selected. So, the middle 70% of all sample means will fall between what two values?

a) 104.8 and 115.2

b) 108.4 and 112.5

c) 115 and 100.7

d) 85 and 125

Answer: a) 104.8 and 115.2

70% Confidence limits

We use z distribution as population standard deviation is given

Mean=μ= 110 garams

Standard deviation =σ= 25 garams

sample size=n= 25

σx=standard error of mean=σ/√n= 5 = ( 25 /√ 25)

Confidence level= 70%

Therefore Significance level=α= 30% =100% -70%

No of tails= 2

This is a 2 tailed test because we are calculating the confidence interval

Z at ...

#### Solution Summary

Three Multiple choice questions on Normal distribution, Confidence Interval are answered.

Statistics - Multiple Choice Questions

See attached file for full problem description.

1. The standard normal distribution

a. is a special case of the normal distribution

b. has a mean equal to 0 and a standard deviation equal to 1

c. measures the distance from the mean in units of the standard deviation

d. all of the above

2. Any normal distribution can be converted to a standard normal distribution by finding

a.  = n 

b. z =  + x 

c. z = ( x -  ) / 

d. x = 

3. The area under the normal curve between 0 and 1 and 0 and -1

a. is the same

b. is negative

c. equal to zero

d. none of the above

4. A z-value is

a. the standard deviation for the standard normal distribution

b. a measure of how many standard deviation the mean is from the median

c. difference of the mean and the probability of z

d. a measure of how many standard deviations a particular score is from the mean

5. The sampling error is

a. the difference between a sample statistic and a population parameter

b. always positive

c. the difference between type I error and type II error

d. the difference between z value and mean

6. A 90% confidence interval for means indicates that 90 out of 100 similarly constructed intervals will include:

a. sample mean

b. sampling error

c. z-value

d. population mean

7. The sample mean is an example of a

a. sample statistic

b. normal population

c. weighted mean

d. population parameter

8. Suppose we have a negatively skewed population. According the Central limit theorem, the distribution of the sample means of a particular size will

a. be negatively skewed

b. form a binomial distribution

c. approach a normal distribution

d. become negatively skewed

9. If the level of confidence is decreased from 95% to 90%, the width of the confidence interval will

a. increase

b. decrease

c. stay the same

d. the level of confidence does not have an effect on the width of the interval

10. The width of the confidence interval is affected by:

a. confidence level

b. sample size

c. variance of the population or sample

d. all of the above

11. The null hypothesis is a claim about

a. size of the sample

b. size of the population

c. value of sample statistic

d. value of population parameter

12. Type I error is committed when

a. p-value is large

b. significance level is greater than 0.05

c. a true Ho is rejected

d. a false Ho is accepted

13. When p-value is smaller than the significance level

a. Type I error is committed

b. Type II error is committed

c. the null hypothesis is rejected

d. critical value cannot be determined

14. A Type II error is

a. Rejecting H1 when it is true

b. Accepting a false Ho

c. Rejecting Ho when it is true

d. Not rejecting a false H1

15. In a test for sample mean,  is not known. Under which of the following conditions can s be substituted for  and z used as a test statistic?

a. when n is 30 or more

b. when n is less than 30

c. when s is known

d. when  is known

16. In a paired t-test, we assume in the null hypothesis that the distribution of the differences between the paired observations have a mean

a. equal to 1

b. equal to n-1

c. equal to 0

d. none of the above

17. Under what conditions would a test be considered a one-tailed test?

a. When Ho contains 

b. When there is more than one critical value

c. When H1 contains -

d. When H1 contains < or >

18. To determine if a diet supplement is useful for increasing weight, the patients are weighed at the start of the program and at the end of the program. This is an example of

a. test of paired differences

b. independent samples

c. one sample test for means

d. two sample test for means

19. The condition or conditions under which null hypothesis is rejected is called

a. the decision rule

b. the likelihood of a Type I error

c. the test statistic

d. the p-value

20. We wish to develop a confidence interval for the population mean. The shape of the population is not known, but we have a sample of 40 observations. We decide to use the 92 percent level of confidence. The appropriate value of z is:

a. 1.96

b. 1.65

c. 2.58

d. 1.75

21. For test of hypothesis for a single sample mean with a one-tailed test using 0.01 significance level in the upper tail, if n = 12, the critical value is:

a. 2.179

b. 2.681

c. 2.718

d. 3.106

22. If a two-tailed test is used, and the significance level is 0.01, the critical value(s) should be:

a. -1.96, 1.96

b. -2.58, 2.58

c. 1.65

d. none of the above

23. In a test of hypothesis for mean, the sample mean is 10, sample standard deviation is 3 and the sample size is 15. The appropriate test statistic is:

a. binomial

b. t value

c. z value

d. none of the above

24. In a two-tailed test, the rejection region is

a. all in the upper tail of the standard normal curve

b. in the lower tail of the standard normal curve

c. divided equally between the two tails

d. -1.96 & 1.96

25. In a simple random sample, each item in the population has

a. to be selected

b. the same chance of being selected

c. a 50% chance of being selected

d. unequal chance of being selected