the scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=536.1μ=536.1 and standard deviation σ=27.9σ=27.9.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 540 or higher?
ANSWER:  

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯x¯, of 35 students?
The mean of the sampling distribution for x¯x¯ is:  
The standard deviation of the sampling distribution for x¯x¯ is:

(c) What z-score corresponds to the mean score x¯x¯ of 540?
ANSWER:

(d) What is the probability that the mean score x¯x¯ of these students is 540 or higher?
ANSWER:  

To estimate the population mean repair cost of microwave ovens in Macomb, a random sample of 9 broken microwave ovens was selected and it is found that the sample mean repair cost is $80 with a sample standard deviation of $15. Answer the following questions:

1) What would be the critical value if you want to find 90 % confidence interval for the population mean?

2) What would be the margin of error if you want to find 90 % confidence interval for the population mean?

3) What would be the length of the 90 % confidence interval?

4) What would happen to 90 % confidence interval if we decrease the sample size from 9-6? Wider or narrower?

Please show how you answered each. Thank you

In the college population, the mean reading comprehension test score is μ = 75 and σ = 25. A researcher wanted to investigate the effect of listening to hip-hop music on reading comprehension. She randomly selected a sample of n = 100 college students. The sample of students completed a reading comprehension test while hip-hop music was played in the background the sample mean reading comprehension score was M = 68. Do the data indicate a significant effect of hip-hop music on reading comprehension? Use a two-tailed z - test with p < .05 to answer this research question.

- Null and alternative hypotheses - All computational steps of the z-test - Critical z-value used for decision about H0

- Decision about H0 (i.e., reject or fail to reject) - If the effect is significant, compute the Cohen's d to establish the size of the effect

- is the effect small, medium or large?

- Conclusion in APA style: interpretation of the z-test outcome to answer the research question. Is there a significant effect of hip-hop music on reading comprehension or not? If there is a significant effect, address in your conclusion the direction of the effect (i.e., is the effect positive or negative/is there an improvement or decline of reading comprehension?) and report the Cohen's effect size.

Explain what a biased sample is and how random sampling reduces the potential of obtaining a sample that is biased. In inferential statistics, why is a biased sample a bad thing?

"iq" "score"
x y
121.892046820712 71.4732161842994
75.3231199290853 12.9190592344864
80.7353976125424 84.9141085286923
91.9095844175845 -42.3921089304488
94.1810816902236 -2.68232999485699
74.5190342941783 -24.2780813181847
118.594093570274 -40.0049484447782
99.1881956204263 0.206020513001461
100.484172827288 -44.9265093418123
96.0242413527543 0.229195593669459
106.144043224744 -2.95492230511574
117.158103938701 -19.2870839962481
79.1373549726252 35.3110928438802
96.541524668086 -23.5780147739683
105.470758811032 49.1522774615725
99.5985999128748 46.5726851253841
104.657509123173 9.48271798764803
86.3158158693298 -25.4269048543043
99.438874992039 -51.9384680082999
100.622681970059 53.3745843562983
79.8678676984686 -25.4750123685849
95.3453801287767 71.6439973612334
141.213862915063 -101.574982678670
100.907577664697 -28.9536302196737
96.2850048629342 0.572812512692053
110.555125562625 -30.6826774054011
126.702100022565 -25.9491611074600
78.116682253087 35.0448127083859
125.763278192055 -75.4365676357808
110.189826539736 -50.4789618210432
120.031830825433 95.441082294667
116.329317367990 -106.118507300053
91.3995403545871 61.7697071542223
67.1717671017129 20.6464837044241
103.956885240671 32.2183861568908
86.8529900060136 -6.62538665297089
112.153597353581 -62.0198332837319
101.544038145957 30.5162192174453
93.6985690141871 35.6366257606887
87.1598523722415 21.8402446324802
103.462616811554 36.4885895758884
93.4347667994378 26.4040057054676
89.2652497474767 63.2711353718747
66.5978405012603 21.6577425446238
118.838468944248 -20.3441512849331
96.1288413662582 44.7060632457826
94.744795827725 30.7193736235243
113.682504871639 -42.5678535029876
105.513774174699 -83.3036944245307
71.8444310751677 -53.5048364428
100.58890486895 56.4962194732963
108.876211777875 103.445235880838
78.9430480237388 7.80940347320373
96.8297678060834 50.0130610322806
113.425045275841 17.7306044850652
86.1697147334069 17.8974687420377
116.037159955396 -42.8320987618029
119.580138905962 110.832617948753
103.338174318402 71.397769967437
87.4542064166235 26.6370103997221
107.931423538019 -62.4291410620053
93.3234404950854 34.1717868832087
109.935414030069 10.5531221389836
96.124422271583 -35.7486297469003
101.206463349905 -21.3592158893932
113.978895298155 -37.6762974283941
92.7129726656618 -1.62518154445572
73.8047499498416 -33.2577669802005
87.6233580483771 -58.7759846722668
102.043095811625 -76.041032261331
84.7637782121371 10.1170348523167
117.250471516515 -98.5203030147308
71.7903904694932 9.04534184739605
76.5910613013864 -33.0924340502142
85.9166485344142 30.3567794392743
73.0204726847607 90.5781558308057
100.757484102641 -35.0482995457613
88.9039906345846 21.8742995725425
115.831258476986 30.1076108060902
125.448279734077 8.19581879558203
83.3852255018193 18.5481168448278
112.092740665462 24.7132055187742
82.700890098919 -1.78898752445938
101.514155078929 57.3348558073038
100.594015128124 -44.1400342860949
103.464058992714 -43.6962212540387
80.4428672192393 -13.4302787051414
104.410590346905 99.2937613397461
115.931753255852 -41.9197152986158
92.289345654039 80.3955269941439
104.806332006923 -32.9543620657468
106.401550000696 -67.8922194894664
89.72709627167 -22.3866457703968
87.080465367208 31.9668321534374
94.7673933618738 21.3618384056050
110.446778275340 84.2311350392016
114.920059002627 43.8621189529085
92.6209783939604 25.4701688798426
112.900465998094 65.3601047313239
78.9561017673847 17.6248371204608

1.2 Conduct a linear regression of "iq" and score.

1.3 Do you reject or fail to reject the null hypothesis about the slope? Why (write a full explanation as discussed in class?

1.4 What is the interpretation of the coefficient for the slope in 1.3?

solve using R.

Suppose that you select a sample of size 20 from a single state and find the mean is 31 (Xbar).

a. What is the upper value for the 95% confidence interval for the population mean (mu) for that state. (Assume the standard deviation (sigma) is the same as it is for the entire country (9.25)

b. What is the lower value for the abouve 95% confidence interval for the population mean (mu) for that state is.

imagine that you have information about how 20 nursing students and 20 psychology students felt about starting PSYC 3002 on Day 1 of this class. You want to know if nursing students and psychology students felt differently about embarking on the Introduction to Basic Statistics journey.

Explain whether you should retain or reject the null hypothesis and why.

data set

In 2018 and 2019, Health Canada commissioned two national surveys on the use of cannabis among people aged 20 to 24. They found 175 users out of the 1000 surveyed individuals in 2018 and 230 out of the 1100 sample in 2019.

(a) Test the hypothesis that there has been a change in the proportion of cannabis users in the 20-24 age

group population between 2018 and 2019. Use the critical value approach and a 0.05 level of

significance.

(b) Find the p-value for your result in (a) above.

(c) Calculate a 95% two-sided confidence interval for the true difference using the data provided.

(d) Explain how the p-value and the confidence interval are or are not consistent with your result in

part (a) above.

A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a jack or ace. ​(b) Compute the probability of randomly selecting a jack or ace or nine. ​(c) Compute the probability of randomly selecting a king or diamond.

Here are summary statistics for randomly selected weights of newborn​ girls: n=164​, x=28.7 ​hg, s=6.3 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level. Are these results very different from the confidence interval 28.0< μ <29.8 hg with only 19 sample​ values, x=28.9 ​hg, and s=1.8 ​hg?

What is the confidence interval for the population mean?

HOUSE OF REPRESENTATIVES

SENATE

COMBINED TABLE – CONGRESS COMBINING HOUSE OF REPRESENTATIVES AND SENATE

Congress if made up of the House of Representatives and the Senate. Members of the House of Representatives serve two year terms and represent a district in a state. The number of representatives each state has is determined by population. States with larger populations have ore representatives than stats with smaller populations. The total number of representatives is set by law at 435 members. Members of the Senate serve sex-year terms and represent a state. Each state has 2 senators, for a total of 100. The tables show the makeup of the 111^th Congress by gender and political party. There are two vacant seats in the House of Representatives.

Please answer the questions below and SHOW YOUR WORK where applicable.. all answers should be proportions rounded to the nearest thousandths (3 decimals) for instance this is what is required to be shown if I ask and answer the following question:

Find the probability that a Senate is a Male or a Democrat:

83/100   +    57/100     –     44/100     =      96/100   =    .960

1. Find the probability that a randomly selected House of Representative is a female.

2. Find the probability that a randomly selected Senator is a female.

3. A House of Representative member is selected at random. Find the probability of each event:
   1. The representative is a male

2. The representative is a Republican

3. The representative is a male GIVEN that the representative is a Republican

4. The representative is female and a Democrat

4. A Senator is selected at random. Find the probability of each event
   1. The senator is a male

2. The senator is not a Democrat

3. The senator is female or a Republican

4. The senator is a male or a Democrat

5. Using the same row and column headings, create a combined table for the Congress (template created for you above)

6. A member of Congress is selected at random. Use the combined table to find the probability of each event.

1. The member is Independent

2. The member is female and a Republican

3. The member is male or a Democrat

Assume that the 129 patients in the Patients dataset represent the entire population of interest. If you were interested in age of the patients and took a sample of 25 patients from this population, what is the standard error of the mean?   What if you took a sample 64 patients from this population, what is the standard error of the mean? What happens to the standard error of the mean as the sample size increases?  If you select a sample of 64 patients, what is the probability that the sample mean is below 75? How to calculate in excel.

Age (Years) 78 74 89 81 87 65 90 61 90 78 78 71 76 76 79 72 72 64 72 69 63 78 83 62 71 83 63 83 76 79 65 79 74 63 84 90 73 81 75 87 70 73 77 71 76 49 78 86 67 69 73 88 67 69 77 64 76 64 41 49 59 81 74 77 (Here is sample of 64 Patients)  

As- sume that the box contains 10 balls: 4 red, 5 blue, and 1 yellow. As in the text, you draw one ball, note its color, and if it is yel- low replace it. If it is not yellow you do not replace it. You then draw a second ball and note its color.

(1) What is the probability that the second ball drawn is yel low?

(2) What is the probability that the second ball drawn is red?

For the following data values below, construct a 98% confidence interval if the sample mean is known to be 9.808 and the population standard deviation is 5.013. (Round to the nearest thousandth) (Type your answer in using parentheses!Use a comma when inputing your answers! Do not type any unnecessary spaces! List your answers in ascending order!) for example: (0.45,0.78)

6.6, 2.2, 18.5, 7.0, 13.7, 5.4, 5.3, 5.9, 4.7, 14.5

2.0, 14.8, 8.1, 18.6, 4.5, 17.7, 15.9, 15.1, 8.6, 5.2

15.3, 5.6, 10.0, 8.2, 8.3, 9.9, 13.7, 8.5, 8.2, 7.9

17.2, 6.1, 13.7, 5.7, 6.0, 17.3, 4.2, 14.7, 15.2, 3.3

3.2, 9.1, 8.0, 18.9, 14.2, 5.1, 5.7, 16.4, 10.1, 6.4

3. We want to estimate the difference between the mean starting salaries for recent graduates with mechanical engineering and aerospace engineering bachelor’s degrees from an university. The following information is provided:

a) A random sample of 49 starting salaries for mechanical engineering graduates produced a sample mean of $64,650 and a standard deviation of $7,000.

b) A random sample of 36 starting salaries for aerospace engineering graduates produced a sample mean of $63,420 and a standard deviation of $6,830.

(1) Find a 95% confidence interval for the difference between the two mean starting salaries.

(2) Someone made a statement that mechanical engineering new graduates make more money than aerospace engineering new graduates on average at the university. Do you agree with the statement? Explain why.