The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and 16. The test is standardized so that the mean score for all children is 100 and the standard deviation is 15. Suppose that the administrators of a very large and competitive school district wish to estimate the mean WISC score for all students enrolled in their programs for gifted and talented children. They obtained a random sample of 40 students currently enrolled in at least one program for gifted and talented children. The test scores for this sample are as follows: 94,106,123,111,127,112,132,107,123,115,133,132,121,109,121,110,107,128,104,118, 111,127,108,119,121,122,102,130,97,111,125,114,99,101,123,124,108,116,144,113 Click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc Use this data to calculate the mean WISC score, ?⎯⎯⎯ , for these 40 students. Next, compute the standard deviation, SD, of the sampling distribution of the sample mean, assuming that the standard deviation of WISC scores for students in the district is the same as for the population as a whole. Finally, determine both the lower and upper limits of a 90% ?-confidence interval for ? , the mean score for all students in the school district who are enrolled in gifted and talented programs. Give ?⎯⎯⎯ and the limits of the confidence interval precise to one decimal place, but give the standard deviation to at least three decimal places in order avoid rounding errors when computing the limits.

x=

SD =

Lower limit =

Upper limit =

The relationship between "strength" and "fineness" of cotton fibers was the subject of a study that produced the following data. (Give your answers correct to two decimal places.) x, Strength 76 69 71 76 83 72 78 74 80 82 y, Fineness 4.3 4.5 4.7 4.0 3.9 4.0 5.0 4.7 4.1 4.5 (a) Draw a scatter diagram. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Find the 95% confidence interval for the mean measurement of fineness for fibers with a strength of 74. Lower Limit Upper Limit (c) Find the 98% prediction interval for an individual measurement of fineness for fibers with a strength of 74. Lower Limit Upper Limit

Twenty-one mature flowers of a particular species were dissected, and the number of stamens and carpels present in each flower were counted. x, Stamens 52 68 70 38 61 51 56 65 43 37 36 74 38 35 45 72 59 60 73 76 68 y, Carpels 21 30 29 19 18 28 31 31 18 24 21 28 29 24 26 22 34 28 32 36 33 (a) Is there sufficient evidence to claim a linear relationship between these two variables at α = .05? (i) Find r. (Give your answer correct to three decimal places.) (iii) State the appropriate conclusion. Reject the null hypothesis, there is not significant evidence to claim a linear relationship. Reject the null hypothesis, there is significant evidence to claim a linear relationship. Fail to reject the null hypothesis, there is significant evidence to claim a linear relationship. Fail to reject the null hypothesis, there is not significant evidence to claim a linear relationship. (b) What is the relationship between the number of stamens and the number of carpels in this variety of flower?. (Give your answers correct to two decimal places.) = + x (c) Is the slope of the regression line significant at α = .05? (i) Find t. (Give your answer correct to two decimal places.) (ii) Find the P-value. (Give your answer bounds exactly.) < p < (iii) State the appropriate conclusion. Reject the null hypothesis, there is not evidence of a significant slope. Reject the null hypothesis, there is evidence of a significant slope. Fail to reject the null hypothesis, there is evidence of a significant slope. Fail to reject the null hypothesis, there is not evidence of a significant slope. (d) Find the 95% prediction interval for the number of carpels that one would expect to find in a mature flower of this variety if the number of stamens were 65. (Give your answers correct to one decimal place.) Lower Limit Upper Limit

Determine the critical values that would be used in testing each of the following null hypotheses using the classical approach. (Give your answers correct to three decimal places.) (a) Ho: ρ = 0 vs. Ha: ρ ≠ 0, with n = 18 and α = 0.05 (smaller value) (larger value) (b) Ho: ρ = 0 vs. Ha: ρ > 0, with n = 32 and α = 0.01 (c) Ho: ρ = 0 vs. Ha: ρ < 0, with n = 16 and α = 0.05

Determine the area under the standard normal curve that lies to the left of ​(a) Z equals 0.19 Z=0.19,

​(b) Z equals negative 0.85 Z=−0.85​,

​(c) Z equals negative 0.04 Z=−0.04​,

and ​(d) Z equals 1.22 Z=1.22.

Perform the following tasks on R Studio/R

Construct a function called conv3 which inputs a measurement in centimeters and outputs the corresponding measurement in inches. However, if a negative value is entered as an input, no conversion of unit is done and an error message is printed instead.

1. Participants saw a series of words on a computer screen. Each time, a word (either relating to a positive emotion or a negative emotion) was presented on a screen for 1500ms. Researchers asked participants to press the “A” key as quickly as possibly if they saw a positive word and the “L” key if they saw a negative word. The response is reaction time in milliseconds (i.e., how long it took the subject to make a response). Use an appropriate test statistical method to answer the question: Did the reaction time differ between the two types of words?

Please resolve the following questions:

1. Identify the independent variable and its associated levels, as well as the dependent variable. (12 pts)
2. Identify the statistical test to be used. (4 pts)
3. State the null and alternative hypothesis. (6 pts)
4. Determine the critical value(s). (4 pts)
5. Calculate the value of your test statistic from the data. (24 pts)
6. Draw a distribution showing your critical regions and test statistic. (7 pts)
7. Make a statistical decision for the hypotheses. (6 pts)
8. Interpret the results and answer/validate the research question - Did the reaction time differ between the two types of words? (12 pts)

A sample has a mean of M = 42 and a standard deviation of s = 3.3, and produces a t statistic of t = 2.04. For a two-tailed hypothesis test that has a critical cutoff T of 1.96, do you reject the null or not?

a. none of the answers are correct

b. there is no way to tell if you can reject or not

c. cannot reject the null hypothesis

d. reject the null hypothesis

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

Upper H 0H0​:

pequals=0.60.6

versus

Upper H 1H1​:

pgreater than>0.60.6

nequals=125125​;

xequals=8080​;

alphaαequals=0.010.01

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Calculate the test​ statistic,

z 0z0.

z 0z0equals=nothing

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y^ (y hat).

Step 4 of 6: Determine the value of the dependent variable y^ at x = 0.

Step 5 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

The following data represents random samples for 7 different treatments. Fill the ANOVA table

, apply the t-test to assess the following statement: "Men and women have different incomes in this city." Show your calculations and copy of the SPSS output in a Word document. In a separate 250-500 Word document, address the following questions: Describe what t-test is the most appropriate and explain why. Discuss whether you used a one-tailed or two-tailed test and explain why. Using SPSS, calculate the t-test and provide the test statistic and critical value assuming an alpha of .05. Calculate the effect size using r2. Interpret the results by (a) stating the reason the study or test was done, (b) presenting the main results, (c) explaining what the results mean, and (d) making suggestions for future research

.

For a standard normal​ distribution, determine the probabilities in parts a through d below.

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a. Find

​P(zless than or equals≤1.561.56​).

​P(zless than or equals≤1.561.56​)equals=nothing

​(Round to four decimal places as​ needed.)

b. Find

​P(zless than or equals≤negative 1.28−1.28​).

​P(zless than or equals≤negative 1.28−1.28​)equals=nothing

​(Round to four decimal places as​ needed.)

c. Find

​P(negative 0.84−0.84less than or equals≤zless than or equals≤1.791.79​).

​P(negative 0.84−0.84less than or equals≤zless than or equals≤1.791.79​)equals=nothing

​(Round to four decimal places as​ needed.)

d. Find

​P(0.340.34less than or equals≤zless than or equals≤2.172.17​).

​P(0.340.34less than or equals≤zless than or equals≤2.172.17​)equals=nothing

2 peas are generated from parents having the green/yellow pair of genes, so there isa 0.75 probability that an individual pea will have a green pod. Find the probabilitythat the number of peas that has a green pod is

(a) at most 8

(b) fewer than 10

(c) more than half of the 12 peas

(d) between 7 to 10 (inclusive)

4) Se cotizó el precio (en dólares) de varios productos similares en el Mercado,
para comparar si existe variación en los precios de dos marcas diferentes A y
B, los datos obtenidos fueron:
Precio Marca A Marca B
10 12 30
30 25 25
50 18 8
70 10 5
90 35 2
Total 100 70
a) Calcule el precio promedio de ambas Marcas. (2 puntos)
b) Cuál de las dos Marcas prese nta mayor variación de precios? (hallar el rango
y desviación estándar) (3 puntos)

The price (in dollars) of several similar products was quoted in the Market, to compare if there is variation in the prices of two different brands A and B, the data obtained were:

Price Brand A Brand B

10 12 30

30 25 25

50 18 8

70 10 5
90 35 2

Total 100 70

a) Calculate the average price of both brands. (2 points)
b) Which of the two brands has the greatest price variation? (find the range and standard deviation) (3 points)