- More data on skittles sales is in. The table shows new daily skittles sales figures.
Mon Tue Wed Thu Fri Sat
13 38 32 35 41 21
- Use c2 to test if skittles sales are different on different days of the week. State the null hypothesis. Give df; test at a = .05
DO BY HAND. NO CREDIT FOR CALCULATOR FUNCTION CALL - Consider the two-variable data
DATA-T (2,3),(3,6),(4,7),(6,10),(7,12) - Draw a scatter plot of the data MAKE A LARGE, NEAT PLOT. SHOW THE SCALE
- Calculate the equation of the line of regression http://batstar.net/idol/equation/yhat.gif
DO BY HAND. GIVE aAND b. WRITE THE EQUATION OF THE LINE - For x = 5 give the expected value of y
- Compute the coefficient of correlation r
- Check 1 gives values of 1, 4, 5, 8; Check 2 gives values of 2, 4, 6, 8; Check 3 gives values of 15, 22, 13, 10
- Use the F table provided and make an ANOVA analysis to verify at 95% the claim that the three checks give the same results
- possible extra credit On the same graph, draw 3 boxplots showing the 3 checks
- A choice with 9 chances — 4 chances of “favorable” versus 5 chances “unfavorable” is repeated 10 times.
- X ~
- Find p (the probability of “full”) and q (the probability of “empty”)
- Find the mean m and the standard deviation s
- Find the chances of exactly 4 “full”
- Find the chances of at most 4 “full”
- Anxiety happens by an exponential distribution on average every 5 months.
- X ~
- Find the probability of anxiety after 4 months.
- Find the 75th percentile for anxiety (for the 75% soonest ‘anxiety’ occasions).
- Suppose X ~ N(100,30)
- Find the probability P(X < 90) USE NORMALCDF
- Graph the distribution MAKE A LARGE, NEAT GRAPH. SHOW SOME POINTS
- Find the 90th percentile.
- A sample of n = 13 items is taken from a population with unknown mean and standard deviation. A mean of`X = 7.2 with a standard deviation of s = 2.5 is found. Give EBM and the 95% confidence interval (two-sided) for m
continued other side
- The Central Limit Theorem for Averages says that sample means`X of size n form a normal distribution
s = 3 has`X = 25. A sample of size n = 16 is taken
[a] Find the standard deviation of the mean
[b] What is the probability that`X is between 24 and 29? - Educational Resources College claims the average matriculating student takes 2.7 years to earn her/his A.A.. From experience you believe it takes longer. You survey 25 students and find a sample mean`X = 3.0 with a sample standard deviation of s = 1.1
- Give the 95% confidence interval (one-tailed) for this claim
— use [0,m + EBM] - Give the p-value for 3.0
- Can you reject the null hypothesis H0: m £ 2.7 (one-tailed)
for a = .05? JUSTIFY WITH NUMBERS - A poll of voters in Side Place finds that 325 of n = 600 contacted “support Unstable Guy”
- Let p represent the proportion of all Side Place voters who support Unstable Guy. Find a point estimate for p
- State the one-tailed hypothesis for predicting (at a = .05) his victory. Explain based on the numbers if you should reject that hypothesis DO BY P-VALUE
GIVE TEST AND PARAMETERS - Unstable Guy wins. Imagine your prediction was incorrect. Explain if that would constitute a Type I error or a Type II error
- 12 greens tested with an average of 7.7 and standard deviation of 2.1
8 yellows tested with an average of 9.3 and standard deviation of 2.0 - Find the standard error
- Find the t-statistic
- With H0: m1 = m2 TWO TAILED find the p-value
- Find whether greens are different than yellows, at 95%? INTERPRET
- 50 squirrels are tested for “walks on sidewalk” and the number found is X1 = 36. 120 squirrels are tested for “stays in tree” and X2 = 61 are found. Test at a = .05 the claim that “walks on sidewalk” occurs more frequently than “stays in tree”
- Get the p-value BE SURE TO GIVE TEST PARAMETERS
- Do you reject the null hypothesis here? JUSTIFY WITH NUMBERS. INTERPRET
- possible extra credit Tom, Dick, and Harry each play the “Win, Lose, Tie” game. Tom does 12-10-8, Dick 6-2-2 and Harry 25-10-15. Test for independence at 95% to see if they all play alike NEED CHI SQUARE: CHECK DEPENDENCY
- possible extra credit Minnie seems to Daisy to have an “attitude.”
She seeks to test that. She gives 100 questionnaires and scores each 1-9. Her null hypothesis is “no attitude” which is m£ 5. Either she rejects the null hypothesis or ahe does not, depending on`X. Suppose she finds that the EBM = 1 at her given a. IN ADDITION TO MEASUREMENT OF ATTITUDE, THERE IS ALSO THE QUESTION OF ACTUALLY HAVING ATTITUDE. Give what kind of error (Type I or Type II) could possibly occur (if the measurement does not match the actual situation)
in the cases below; describe how that would be a mistake EXPLAIN CLEARLY - Daisy’s test gives `X = 7
- Daisy’s test gives `X = 3
- 14 red cards tested with an average of 5.0 and standard deviation of 1.1
while 21 black cards tested with an average of 4.4 and standard deviation of 1.0 - Find the standard error USE FORMULA PROVIDED
- Find the t-statistic USE FORMULA PROVIDED
- With H0: m1 = m2 GIVE FUNCTION CALLTWO SIDED find the p-value
- Do we reject at 95%? EXPLAIN HOW BLACK TESTS COMPARED TO RED
- 100 squirrels are tested for runs on sidewalk and the number found is X1 = 40. 120 squirrels are tested for stays in tree and the number found is X2 = 63. Test at a = .05 the claim that runs on sidewalk occurs in the same proportion as stays in tree
- Give the null hypothesis for the claim equal proportions
MEASURE IS DON’T REJECT - Get the p-value for equal proportions SHOW FUNCTION CALL; INTERPRET
- Give the null hypothesis for the claim stays in tree is more common
MEASURE IS REJECT “LESS COMMON” - Get the p-value for stays in tree being more common
SHOW FUNCTION CALL; INTERPRET - Data on Wholesome sales is in. New daily Wholesome sales figures are shown in the table.
Mon Tue Wed Thu Fri Sat
34 41 30 26 7 12
Use c2 to test if Wholesome sales are different on different days of the week.- State the null hypothesis. Give df
- Test at a = .05
DO BY HAND USING TABLE PROVIDED — NOT BY CALCULATOR FUNCTION CALL
extra credit
- Three visits occur —
Visit 1 gives values of 6, 5, 9
Visit 2 gives values of 27, 13, 10
Visit 3 gives values of 1, 2, 2, 5
Use the F table provided and make an ANOVA analysis to verify at 95% the claim that the three visits perform similarly
EXPLAIN THE MEANING OF ‘REJECT’ OR ‘NOT REJECT’ — WHICHEVER OCCURS
- 20 buns tasted with an average of 5.0 grams sugar and standard deviation of 2.1
while 15 rolls tasted with an average of 6.2 grams sugar and standard deviation of 1.4 - Find the standard error USE FORMULA PROVIDED
- Find the t-statistic USE FORMULA PROVIDED
- With H0: m1 = m2 GIVE FUNCTION CALL FOR 2SAMP-T
MAKE TWO SIDED find the p-value - Say if we reject at 95%? EXPLAIN HOW BUNS COMPARED TO ROLLS IN SUGAR CONTENT
- Bill sells workplace coffee.
Daily average sales are shown in the table (number of cups sold).
Mon Tue Wed Thu Fri
19 14 16 21 30
Use c2 to test if coffee sales are different on different workdays.- State the null hypothesis. Give df
- Test at a = .05
DO BY HAND USING TABLE PROVIDED — NOT BY CALCULATOR FUNCTION CALL
- Three “people checks” happen:
Check 1 finds 4, 6, and 10 items
Check 2 finds 22, 15, 11, and 12 items
Check 3 finds 1, 7, 12 items
Use the F table provided (with a = .05) and make an ANOVA analysis to verify at 95% the claim that the three checks find items similarly
EXPLAIN THE MEANING OF ‘REJECT’ OR ‘NOT REJECT’ — WHICHEVER OCCURS
- Suppose X ~ N(20,4)
- Graph that distribution. NEEDS BIG GRAPH AND APPROPRIATE SCALE. GRAPH POINTS (X,Y) – MAKE TABLE
- Find the probability P(X < 17) USE NORMALCDF
- Find the probability P(X < 12) USE Z SCORE TABLE
- Find the z associated with X = 22
- Find the 85th percentile
- For theoretical reasons [the CLT], we say that when we sample means`X from a set of samples each of size n we tend to get a normal distribution
A sample of size n = 25 is taken - Find the standard deviation of the mean
- Give the probability that`X is between 25 and 34
- Give the probability that an individual data point X is between 25 and 34
- A sample of n = 15 items is taken from a population with unknown mean and standard deviation.
A mean of`X = 7.4 with a standard deviation of s = 2.6 is found - Give the 95% confidence interval (two-sided) for m
- Abe claims that the average for samples of that size from that population is “really” at least 9
Find the p-value for Abe’s claim, with given data
TO REJECT OR NOT REJECT — THAT IS THE QUESTION - Barbara says that “most people like good coffee.” In a survey, she finds that 41 of 104 people concur.
- Justify with numbers that the data fails – at 99% – to validate her claim.
- Should most people “actually” like good coffee, state whether
that would constitute a Type I or a Type II error for Barbara’s survey
- Peter sees at least 3 squirrels a day outside his window. For twenty (20) days
he records his “squirrel count” and gets an average of just 2.2 with
an observed standard deviation of s = 1.3 - Let H0: m ³ 3 be the null hypothesis. Using the T-Test find the p-value
CITE PARAMETERS USED - At 95% is Peter’s claim justified? EXPLAIN
- A voter survey finds that 58% favor the candidate Alpha, while 42% favor candidate Beta
- With n = 400 and assuming good experimental design, say what the local newspaper editor would do for a 90% confidence interval for the election result TWO-SIDED
- Use 1PROPZ Test to evaluate the claim of Alpha’s campaign manager, that Alpha will win with 95% confidence YES/NO. ONE-SIDED. GIVE FUNCTION CALL PARAMETERS
FORMULAS
- Suppose X ~ N(80,20)
- Graph this distribution. NEEDS BIG GRAPH AND APPROPRIATE SCALE — SHOW POINTS
- Find the probability P(X < 72) USE Z SCORE
- Find the probability P(X < 70) USE NORMALCDF
- Find the z associated with X = 64
- Find the 60th percentile
- For theoretical reasons, we say that when we sample means`X from a set of samples each of size n we tend to get a normal distribution
- Find the standard deviation of the mean
- What is the probability that`X is between 9 and 11?
- The Law of Large Numbers says as samples get larger then the standard deviation of the mean gets smaller.
What size n is needed to get the standard deviation of the mean down to 0.1? - Students in Math 10 get an average of `X = 6.0 on their exam, with a standard deviation s = 1.7. A sample of 7 students sitting on the left is taken. Assume exam grades are normally distributed
- Using the C.L.T., find the standard deviation of the average of the sample.
- If z = 0.8 is required for attaining an “A-/B+” level, find the exam score needed for that outcome ROUND UP TO ONE DECIMAL PLACE
- According to the Substance Abuse and Mental Health Services Administration (SAMHSA), people identified as “seriously mentally ill” die on average 25 years earlier than the general U.S. population. A sample of the records of n = 100 such people is taken which confirms that average with s = 15
- `X ~
- Find the chance of a person thus identified living as long as the average person in the population
- Find the chance that a sample of n = 400 (also with s = 15) would have an average life span difference less than 22.5 years
- EXTRA CREDIT Cars enter a freeway on ramp at speeds uniformly distributed from 30 to 60 mph
- In other words, X ~
- Find m and s
- A sample of n = 36 cars averages 50 mph. For this sample, `X ~
- Find the standard deviation of the mean for this sample
- Find the probability that the sample average will be as large or larger than the average found
- A box holds the 9 hearts {2,3,4,5,6,7,8,9,10}. Let E = {2,3,6,10}, F = {2,3,5,8}, and G = {4,7,9,10}
- Use the formula for mutual exclusion (not: the addition rule) to establish that F and G
are mutually exclusive events - Use a formula for independence (not: the product rule) to establish that E and G
are/are not independent events
Note that explicit description of sets and calculations is expected.
Numbers are needed to establish results, and those should be suitably explained
- Consider the data sample DATA-E 6,10,18,6,20,15,21,16,19,16,25,16,20,21,8,19
- Give n
- Make a frequency table, a relative frequency table, and a cumulative relative frequency table for the data
- Select a systematic sample: Use the original data
as presented (not sorted) and list every successive 4th datum
STARTING WITH THE SECOND DATUM
NOTE: DO NOT USE THE SORTED VERSION OF THE TABLE - Find the median of the systematic sample.
Contrast with the median of DATA-E - You guess on a t/f exam with 10 questions.
- X ~ B(n,p) give the values of the variables
- Find the probability you get 50% SHOW SETTINGS FOR BINOMPDF
- Find the probability of “passing” — at most 3 unfavorable.
AGAIN, SHOW SETTINGS. USE BINOMCDF
That is the chance of passing the test
- You see the cougar according to an exponential distribution on the average every 8 weeks Find the probability of seeing the cougar within a period of six weeks
- A DeAnza College student figures there is a 10% chance of parking in a favorite space in the A lot The student will try parking day after day until she/he succeeds in parking in that space
- X =
- X ~
- Find the probability of first parking in the space after exactly 4 attempts
- A normal distribution has m = 10 s = 2. Give the probability that the outcome is between 6 and 9, to (at least) three decimal places
- A box contains the 4,5,6 of diamonds and the 6,7,8,9 of hearts. Two cards are drawn (w/o replacement) Let S = the first card is 6, D = the first card is a diamond, E = the second card is a heart, F = the second card is a 4,
- Find P(S)
- Find P(S|D)
- Find P(S|F)
- Show that E and F are mutually exclusive USE FORMULA FROM OTHER SIDE. GIVE NUMBERS
- You roll a (fair) die, which has 6 faces, and then flip a coin, which gives H or T. Let K = outcome is “coin is 'T' and die is less than '4'” and L = outcome is “die is bigger than '4',”
- List the sample space THIS IS A FAIRLY LONG LIST Give n
- Find P(K)
- List the favorable outcomes for L
- Show that “coin is H” is independent of L USE FORMULA. GIVE NUMBERS
- Show that “coin is H” is not independent of K USE FORMULA GIVE NUMBERS
- A choice “with 7 options” — 5 being “alpha” [success] while 2 options are “beta” [failure] — is repeated 8 times.
- Possible values are X =
- X ~
- Find p and q.
- Find the mean m and the standard deviation s.
- Find the chances of exactly 3 “alphas.” SHOW FUNCTION CALL
X 1 2 3 4
P(X) .5 .1 .3 .1
- Let X be a discrete random variable satisfying:
- Find the mean (expected value) m
- EXTRA CREDIT
Find the standard deviation s
FOR [a] AND [b] YOU MUST COMPLETE THE TABLE
- Acts of Madness happen from an exponential distribution on the average every 4 months.
- X =
- X ~
- Graph this distribution. NEEDS BIG GRAPH AND APPROPRIATE SCALE.
- Find the probability that an act of madness happens after 3 months.
- Find the 80th percentile for acts of madness (viz. for the 80% soonest such acts).
- Find the probability that an act of madness happens between 6 and 10 months.
for extra credit
- A DeAnza College student figures to have a 20% chance of having a ‘good experience’ sitting at the fountain in the Quad. The person intends to sit again and again until a ‘good experience’ occurs
- X =
- X ~
- Find how many times on average the person must sit to expect a ‘good experience’
- Find the probability the person will have that experience in no more than 4 tries
10 years ago
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