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On the basis of previous research and sound theoretical considerations, a cognitive psychologist believes that memory for pictures is superior to memory for words. To test this, the psychologist performs and experiment in which students from an Intro to Psych. course are used as subjects. 8 randomly selected students view 30 slides with nouns printed on them, and another group of 8 randomly selected students views 30 slides with pictures of the same nouns. Each slide contains either one noun or one picture and is viewed for 4 seconds. After viewing the slides, subjects are given a recall test, and the number of correctly remembered items is measured. The data follow:
# of Pics # of Nouns Recalled Recalled 18 12 21 9 14 21 25 17 23 16 19 10 26 19 15 22 A) What is the directional alternative hypothesis? B) What is the null hypothesis? C) Using a=0.05 (1Tail), what is your conclusion? D) Estimate size of the real effect. |
A) The alternative hypothesis states that memory for pictures is superior to memory for words (Mu) 1 > (Mu) 2
B) The null hypothesis states that memory for pictures is not superior to memory for words (Mu) 1 (Less than or equal to sign) (Mu) 2 C) tobt = 1.86 and tcrit= 1.761 Since |tobt| > 1.761, Reject Ho and conclude that memory for pictures is superior to memory for words. D) d^ (d-hat) =0.93 This is a large effect, according to cohen's criteria. |
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The director of H.R. at a large company is considering hiring part-time employees to fill jobs previously staffed with full time workers. However, he wonders if doing so will affect productivity. Therefore, he conducts an experiment to evaluate the idea before implementing it factory-wide. Siz full-time job openings, from the parts manufacturing division of the company, are each filled with two employees hired to work half-time. The output of these six half-time pairs is compared with the output of a randomly selected sample of six full-time employees from the same division. Note that all employees in the experiment are engaged in manufacturing the same parts. The avg. number of parts produced per day by the half-time pairs and full-time workers is shown here:
Parts Produced Per Day 1/2 Time Full-Time Pairs 24 20 26 28 46 40 32 36 30 24 36 30 Does the hiring of the part-time workings affect the productivity? Use a=0.05(2tail) in making a decision. |
Tobt=0.60 and tcrit = (+or-) 2.228. Since |tobt| < 2.228, we retain Ho. Based on these data, we cannot conclude that hiring part-time workers instead of full-time workers will affect productivity.
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A sample set of 29 scores has a mean of 76 and a std. dev. of 7. Can we accept the hypothesis that the sameple is random from a from a population greater than 72? Use a=0.01 (1Tail) in making the decision.
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Tobt = 3.08, and tcrit with 28 df= 2.467. Since |tobt| > 2.467 we can reject Ho, which specifies that the sample is a random sample from a population with a mean (less than or equal to) 72. Therefore, we can accept the hypothesis that the sample is a random sample from a population with a mean > 72.
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Using each of the following random samples, determine 95% and 99% confidence intervals for the population mean:
A) Xbar obt =25, s=6, N= 15 B) Xbar obt =120, s=8, N=30 C) Xbar obt =30.6, s=5.5, N=24 D) Redo part a with N=30. What happens to the CI as N increases? |
95% 99%
A) 21.68-28.32 20.39-29.61 C) 28.28-32.92 27.45-33.75 D)22.76-27.24 21.98-28.02 |
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A local business school claims that its graduating seniors get higher paying jobs than the national avg. for business school grads. Last year's figures for salaries paid to all business school grads. on their first job showed a mean of $10.20 an hour. A random sample of 10 grads from last year's class of local business school showed the following hourly salaries for their first job: $9.40, $10.30, $11.20, $10.80, $10.40, $9.70, $ 9.80, $10.60, $10.70, $10.90. You are skeptical of the business school claim and decide to evaluate the salary of the business school graduates using a=0.05(2Tail) what do you conclude?
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Tobt = 0.98 and tcrit = (+-) 2.262. Since |tobt|<2.262, we retain Ho. From these data, we cannot conclude that the graduates for the local business school get higher salaries for their first jobs than the national avg.
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If a population of raw scores is normally distributed and has a mean (mu) =80 and a std. dev (sigma) = 8, determine the parameters (Mu sub-xbar and sigma sub-xbar) of the sampling distribution of the mean for the following sample sizes:
A) N=16 B) N=35 C) N=50 D) Explain what happens as N gets larger. |
A) The distribution is normally shaped. Mu sub-xbar=80, Sigma sub-xbar=2.00
B) The distribution is normally shaped. mu sub-xbar=80, sigma sub-xbar= 1.35 C) Normal. mu sub-xbar=80, sigma sub-xbar=1.13 D) As N increases mu sub-xbar stays same but sigma sub-xbar decreases. |
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A professor has been teaching statistics for many years. His records show that the overall mean for the final exam scores is 82, with a std. dev. of 10. The professor believes that this year's class is superior to his previous ones. The mean for the final exam scores for this years class of 65 students is 87. Use a=0.05(1Tail) what do you conclude?
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Zobt= 4.03 zcrit= 1.645. Since |zobt| < 1.645 reject Ho. Conclude that this years class is superior to previous ones.
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The manufacturer of brand A jogging shoes wants to determine how long the shoes last before resoling is necessary. She randomly samples from users in Chicago, NYC, and Seattle. In Chicago, the sample size was 28 and the mean duration before resoling was 7.2 months. In NYC, the sample size was 35 and the mean before resoling was 6.3 months. In Seattle, the sample size was 22 and the mean before resoling 8.5 months. What is the overall mean duration before resoling is necessary for brand A jogging shoes?
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7.17 Months
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For the following distributions, state whether you would use the mean or the median to represent the central tendency of the distribution. Why?
A) 2,3,8,5,7,8 B) 10,12,15,13,19,22 C) 1.2,.8,1.1,.6,25 |
A) mean-no extreme scores
B) mean C) median-25 is an extreme score in the distribution here. |
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If N=12 and P=50.
A) What is the probability of getting exactly 10 P events? B) What is the probability of getting 11 or 12 P events? C) What is the probability of getting at least 10 P events? D) What is the probability of getting a result as extreme or more extreme than 10 P events? |
Using Table B
A) 0.0161 B) 0.0031 C)0.0192 D) 0.0384 |
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An individual flips 9 coins. If she only allows only a head or tail with each coin:
A) What is the probability they will all be heads? B) What is the probability there will be seven or more heads? C) What is the probability there will be a result as extreme or more extreme than seven heads? |
A) 0.0020
B) 0.0899 C)0.1798 |
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You are interested in determined whether a particular child can discriminate the color green from blue. Therefore, you show the child 5 wooden blocks. The blocks are identical except that two are green and three are blue. You randomly arrange the blocks in a row and ask him to pick out a green block. After a block is picked, you replace it and randomize the order. Ask him to pick a green block again. Continue process until 14 selections are made. If he really cant discriminate green from blue, what is the probability he will pick a green block at least 11 times?
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0.0039
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In your voting district, 25% of the voters are against a particular bill and the rest favour it. If you randomly poll four voters from your district, what is the probability that:
A) None favour the bill? B) All favour the bill? C)At least one will be against the will? |
A) 0.0039
B) 0.3164 C)0.6836 |
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A leading toothpaste manufacturer advertises that, in a recent medical study, 70% of the people tested had brighter teeth after using its toothpaste (called Very Bright) as compared with a leading competitior's (called Brand X). The advertisement continues, "Therefore, use Very Bright and get brighter teeth." In point of fact, the data upon which these statements were based were collected from a random sample of ten employees from the manufatcturer's Pasadena plant. In the experiment, each employee used both toothpastes. Half of the employees used Brand X for three weeks, followed by Very Bright for the same time period. A brightness test was given at the end of each 3-week period. Thus, there were two scores for each employee, on from the brightness test following the use of Brand X, and one following the use of Very Bright. The following table shows the score (the higher, the brighter):
Subject Very Bright Brand X 1 5 4 2 4 3 3 4 2 4 2 3 5 3 1 6 4 1 7 1 3 8 3 4 9 6 5 10 6 4 A) What is the directional, alternate hypothesis? B) What is the null hypothesis? C) Using a=0.05(1Tail), what might you conclude? D) What error might you be making in your conclusion in part C? E) To what population does your conclusion apply? F) Does the advertising seem misleading? |
A) The alternative hypothesis states that using Very Bright toothpaste instead of Brand X results in brighter teeth.
B) The null hypothesis states that both brands are equal or Brand X is better. C) p(7 or more pluses) = 0.1719>0.05, retain Ho. You cannot conclude that very bright is better. D) You may be making a Type II Error, retaining Ho if it's false. E) The results apply the the employees of the Pasadena plant at the time of the experiment. |
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A gumball dispenser has 38 orange gumballs, 30 purple gumballs, and 18 yellow ones. The dispenser operates such that one quarter delivers one gumball.
A) Using three quarters, what is the probability of obtaining three gumballs in the order prange, purple, orange? B) Using one quarter, what is the probability of obtaining 1 gumball that is either yellow or purple? C) Using three quarters, what is the probability that of the three gumballs obtained, exactly one will be purple and one will be yellow? |
A) 0.0687
B) 0.5581 C) 0.2005 |
