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# Normal Probability, Confidence interval & Hypothesis Testing

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I. Matching
a. Nominal _____1. Number of pages in a book
b. Ordinal _____2. Name of a book
c. Discrete _____3. Weight of a book
d. Continuous _____4. Rank on bestsellers list

II. Which of the following is not like the others in the group and say why:
mean, standard deviation, median, mode, and midrange

III for a set of ordered pairs the prediction line has b0 = 1 and b1 = 2.
We also have that one of the ordered pairs is (7, 16)
1. compute the fit
2. compute the residual

IV. Does a strong correlation prove cause and effect or not?

V. Suppose b1 is negative. What can we conclude about r
1. It is negative.
2. it is 0
3. it is positive
4. none of the above

VI. If P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.15, what is P(A|B)?

VII. You may make a Venn diagram or a table or both, but SHOW YOUR WORK
You will be hoping for a merit scholarship (M) or an athletic scholarship (A).
They say the chance of getting an athletic scholarship is 0.2
Then they say the chance of getting both an athletic scholarship and a merit scholarship is 0.05
Then they say the chance of getting one or the other is 0.5.

a. P(M) =
b. P(not A and not M) =
c. P(M|A) = (I want the ratio)
d). P(A|M) = (I want the ratio)
e. Are A and M independent? Show why you say so

VIII If A and B are mutually exclusive events with P(A) = .0.40, then P(B)
a. can be any value between 0 and 1
b. cannot be larger than 0.40
c. cannot be larger than 0.60
d. cannot be determined

IX what is the mean of the standard normal distribution (the z scores)?

X what is the approximate area under the curve between &#956; - 3&#963; and &#956; + 3&#963;?

XI what is the area under the standard normal curve between -2.41 and - 1.24?

XII Find P(z > -0.24)

XIII what z score corresponds to the 80th percentile?

XIV. If the mean of a normal distribution is 300 and the standard deviation is 50, what percentage of the scores is between 270 and 320?

XV .If it is known that college students sleep an average of 6 hours per night with a standard deviation of 1.8
1. find the probability that she sleeps between 5 and 8 hours.
2. Find the probability that she sleeps more than 7 hours

XVI
1.As the sample size increases, which happens, the sampling distribution gets more or less peaked in the middle?
2. As the sample size increases, which happens, the tails get larger or the tails get smaller?

XVII consider the confidence intervals to be alike in every way except the part I say changes and a change for part 1 does not apply for part 2
1. which is longer, a confidence interval for sample size n = 16 or n = 25?
2. which is longer, a confidence interval for 90% confidence or for 99% confidence?

XVIII. when we talk about a 95% confidence interval, what does that mean? 95% of what do what?

XIX A soft drink machine is set to dispense soft drink labeled 16 oz. If the mean is 16.1 oz with a standard deviation of 0.0.15 oz
1. what are the upper and lower limits for the 90% confidence interval for 1 bottle?
2. what are the upper and lower limits for the 90% confidence interval for a sample of size n = 20?

XX. Will a confidence interval for &#956; always contain the point estimate or not?

XXI If you have rejected the null hypothesis when it is false, then you have made
a. a type A correct decision
b. a type B correct decision
c. A type I error
d. A type II error

XXII
1. In a hypothesis test, if &#945; = 0.01 and p-value = 0.019, do you have significant evidence to reject the null hypothesis or not?
2. in a hypothesis test, if &#945; = 0.05 and the p-value = 0.042, do you have significant evidence to reject the null hypothesis?
3. Do large or small values for the p-value support the alternative hypothesis?

XXIII. Give the null and alternative hypotheses for the two tail test for the following claim "the mean of the ACT scores is 25

XXIV Which t-distribution is most like the normal curve, the one for df = 10 or n = 20?

XXV which two T VALUES bracket 2.50 on the df = 15 distribution?

XXVI pretest versus post test (before and after studies) are usually used for
a. dependent samples
b. independent samples
c. either one
d. neither applies

XXVII. consider the following set of paired data and calculate the value of A - B
A 1 3 4 4 5
B 3 5 4 1 2
A - B

XXVIII If a confidence interval for the difference of 2 proportions contains both positive and negative numbers, what does that tell you?

XXIX Only 48 out of 200 people interviewed were able to name the Secretary of State of the United States. Find the values of
x =
n =
p'
q'

XXX Here are expected values for a chisquared &#967;2 test
41 44
72 71

1. Compute the expected value for the cell in the first column, first row
2. show the formula and plug in the numbers for computing the addend for chisquared for the first column and the first row.
3.how many degrees of freedom does this test have?

4. If we had the chisquared sum = 24 with df = 15, WHICH TWO VALUES FROM THE TABLE WOULD BRACKET THE P VALUE?

XXXI Can we use an ANOVA test to see whether our linear model is good in regression? There is no work to show, but tell me why you think you are right.

**Real ANOVA question

I give you the df and SS numbers. I want the MS numbers and the F number. You don't have enough information to find the p-value
Source df SS MS F
Model 2 29.20
Error 12 136.13

https://brainmass.com/statistics/quantative-analysis-of-data/normal-probability-confidence-interval-hypothesis-testing-272416

#### Solution Preview

I. Matching
a. Nominal c. 1. Number of pages in a book
b. Ordinal a 2. Name of a book
c. Discrete d 3. Weight of a book
d. Continuous b 4. Rank on bestsellers list

II. Which of the following is not like the others in the group and say why:
mean, standard deviation, median, mode, and midrange

Standard deviation is not like the other measures. Standard deviation measure the dispersion while all others measure central tendency.

III for a set of ordered pairs the prediction line has b0 = 1 and b1 = 2.
We also have that one of the ordered pairs is (7, 16)
1. compute the fit
2. compute the residual

Fit Y = b0+b1X = 1+2*7 =15

Residual = observed -Fit = 16-15 =1

IV. Does a strong correlation prove cause and effect or not?

No.
1. A may be the cause of B.
2. B may be the cause of A.
3. some unknown third factor C may actually be the cause of both A and B.

V. Suppose b1 is negative. What can we conclude about r
1. It is negative.
2. it is 0
3. it is positive
4. none of the above

VI. If P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.15, what is P(A|B)?

P(A|B) =P(AB) /P(B) = 0.15/0.30 =0.50

VII. You may make a Venn diagram or a table or both, but SHOW YOUR WORK
You will be hoping for a merit scholarship (M) or an athletic scholarship (A).
They say the chance of getting an athletic scholarship is 0.2
Then they say the chance of getting both an athletic scholarship and a merit scholarship is 0.05
Then they say the chance of getting one or the other is 0.5.

a. P(M) = 0.30
b. P(not A and not M) = 1-0.50 =0.50
c. P(M|A) = (I want the ratio) = P(MA) /P(A) = 0.05 / 0.2 =0.25
d). P(A|M) = (I want the ratio) = P(MA) /P(M) = 0.05/0.30 =0.1666
e. Are A and M independent? Show why you say so
Here 0.05 =P(MA) ≠ P(M)*P(A) =0.30*0.20
Thus A and M are not independent

VIII If A and B are mutually exclusive events with P(A) = .0.40, then P(B)
a. can be any value between 0 and 1
b. cannot be larger than 0.40
c. cannot be larger than 0.60
d. cannot be determined

IX what is the mean of the standard normal distribution (the z scores)?
Mean =0

X what is the approximate ...

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval, normal probability and test statistic. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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