The diameter of holes for cable harness is known to have a standard deviation of 0.01 in. A random sample of size 10 yields an average diameter of 1.5045 in. Use α=0.01 to:

a. Test the hypothesis that the true mean whole diameter equal 1.5 in.

b. What sample size would be necessary to detect a true mean hole diameter of 1.505 in. with probability of at least 0.95?

c. What is the type II error if the true mean hole diameter is 1.504 in.?

#33-36, use the following information. Test the claim that the mean female reaction time to a highway signal is less than 0.7 s. When 18 females are randomly selected and tested, their mean is 0.668 s. Assume that σ = 0.1 s, and use a 5% level of significance. 33. Give the null hypothesis in symbolic form. (a) H0 :µ < 0.7 (b) H0 :µ > 0.7 (c) H0 :µ ≤ 0.7 (d) H0 :µ ≥ 0.7 (e) H0 : p ≥ 0.7 34. Determine the appropriate test statistic. (a) z = 1.528 (b) z = −1.645 (c) z = −1.36 (d) t = 0.971 (e) t = −1.74 35. Find the appropriate critical value(s). (a) z = −1.96 (b) z = 1.645 (c) z = −1.645 (d) t = 1.74 (e) t = −1.74 36. Make the appropriate decision. (a) Reject H0 (b) Fail to reject H0

The probability that a given 20-35 year old survives a given viral infection is 99%. • The probability that a given 65-80 year old survives the same viral infection is 95%. • In a group of 20 20-to-35-year-olds with the viral infection, what is the probability that all 20 will survive? • In a group of 20 65-to-80-year-olds with the infection, what is the probability that all 20 will survive?

The data below shows the sugar content in grams of several brands of​ children's and​ adults' cereals. Create and interpret a​ 95% confidence interval for the difference in the mean sugar​ content,

mu Subscript Upper C Baseline minus mu Subscript Upper AμC−μA.

Be sure to check the necessary assumptions and conditions.​ (Note: Do not assume that the variances of the two data sets are​ equal.)

Height vs Weight - Erroneous Data: You will need to use software to answer these questions.

Below is the scatterplot, regression line, and corresponding data for the height and weight of 11 randomly selected adults. You should notice something odd about the last entry.

You should be able copy and paste the data by highlighting the entire table.

Answer the following questions regarding the relationship.

(a) Using all 11 data pairs for height and weight, calculate the correlation coefficient. Round your answer to 3 decimal places.
r =

(b) Is there a significant linear correlation between these 11 data pairs?

YesNo    

(c) Using only the first 10 data pairs for height and weight, calculate the correlation coefficient. Round your answer to 3 decimal places.
r =

(d) Is there a significant linear correlation between these 10 data pairs?

YesNo    

(e) Which statement explains this situation?

The height for the last data pair must be an error.The erroneous value from the last data pair ruined a perfectly good correlation.    Despite the low correlation coefficient from part (a), there is probably a significant correlation between height and weight.All of these are valid statements.

Additional Materials

Law of Supply: You will need to use software to answer these questions.

The Law of Supply states that an increase in price will result in an increase in the quantity supplied (assuming all other factors remain unchanged). Below is the scatterplot, regression line, and corresponding data for price (x) -vs- quantity supplied (y).

You should be able to copy and paste the data by highlighting the entire table.

Answer the following questions regarding the relationship.

(a) Using all 12 data pairs for x and y, calculate the correlation coefficient. Round your answer to 3 decimal places.
r =

(b) Is there a significant linear correlation between these variables?

YesNo    

(c) Use software to find the regression equation. What is the slope and y-intercept? Round each answer to one decimal place.

(d) Use the regression equation to estimate the quantity supplied if the price is set at $5.00. Round your answer to the nearest whole number.
ŷ =  units

A researcher tested whether aerobics increased the fitness level of eight undergraduate students participating over a 4-month period. Students were measured at the end of each month using a 10-point fitness measure (10 being most fit). The data are shown here. Conduct an ANOVA to determine the effectiveness of the program, using alpha = .05. Use the Bonferroni method to detect exactly where the differences are among the time points (if they are different).

A sample of 30 houses that were sold in the last year was taken. The value of the house (Y) was estimated. The independent variables included in the analysis were the number of rooms (X1), the size of the lot (X2), the number of bathrooms (X3), and a dummy variable (X4), which equals 0 if the house does not have a garage and equals 1 otherwise. The following results were obtained: Coefficients Standard Error Intercept 15,232.5 8,462.5 X1 2,178.4 778.0 X2 7.8 2.2 X3 2,675.2 2,229.3 X4 1,157.8 463.1 Analysis of Variance DF SS MS Regression 204,242.88 51,060.72 Residual (Error) 205,890.00 8,235.60 Test whether or not there is a significant relationship between the value of a house and the independent variables. Use a 0.05 level of significance. Be sure to state the null and alternative hypotheses. (f) Test the significance of β1 at the 5% level. Be sure to state the null and alternative hypotheses. (g) Compute the coefficient of determination and interpret its meaning. (h) Estimate the value of a house that has 9 rooms, a lot with an area of 7,500, 2 bathrooms, and 2 garages.

Suppose the life span of a light bulb is normally distributed with mean 1000 hours and standard deviation 75 hours. (a) Find the 57th percentile of this distribution. (b) Find the probability that a random light bulb will last longer than 1100 hours. (c) Find the probability that the life span of a light bulb will be more than 3.14 standard deviations away from the mean. (d) Suppose you take a sample of 15 light bulbs and measure the average life span. Carefully justify whether the Central Limit Theorem applies, and if it does, find the probability that the average life span is between 950 and 1025 hours.

A baseball​ pitcher's most popular pitch is a​ four-seam fastball. The data below represent the pitch speed​ (in miles per​ hour) for a random sample of 15 of his​ four-seam fastball pitches.

85.5, 86.8, 93.1, 93.6, 88.7, 92.8, 86.4, 93.7, 89.9, 91.2, 86.7, 93.9, 85.4, 87.4, 90.6

(a)

Using the correlation coefficient of the normal probability​ plot, is it reasonable to conclude that the population is normally​ distributed?

Since the absolute value of the correlation coefficient between the expected​ z-scores and the ordered observed​ data, ____, ____ (exceeds/ does not exceed) the critical value ___, it (is/ is not) reasonable to conclude that the data come from a population that is normally distributed. (Round three decimal places)

(b) Construct and interpret a​ 95% confidence interval for the mean pitch speed of the​ pitcher's four-seam fastball.

One can 95% confident that the mean pitch speed of the pitcher's four-seam fastball is between ___ and ___ miles per hour.

One can 90% confident that the mean pitch speed of the pitcher's four-seam fastball is between ___ and ___ miles per hour.

One can 99% confident that the mean pitch speed of the pitcher's four-seam fastball is between ___ and ___ miles per hour.  

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 76 students in the highest quartile of the distribution, the mean score was x = 178.10. Assume a population standard deviation of σ = 8.21. These students were all classified as high on their need for closure. Assume that the 76 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 2.1 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.)

Q7: (About Interval Estimation: 2 marks) A coin is flipped 100 times, and 42 heads are observed. Find a 99% confidence interval of π (the true population proportion of getting heads) and draw a conclusion based on the collected data. Hint: Choose the best one. (0.274, 0.536) a 99% confidence interval of π and we conclude it is a fair coin. (0.293, 0.547) a 99% confidence interval of π and we conclude it is a fair coin. (0.304, 0.496) a 99% confidence interval of π and we conclude it is a fair coin. (0.324, 0.486) a 99% confidence interval of π and we conclude it is a fair coin. (0.433, 0.509) a 99% confidence interval of π and we conclude it is a fair coin. (0.274, 0.536) a 99% confidence interval of π and we conclude it is not a fair coin. (0.293, 0.547) a 99% confidence interval of π and we conclude it is not a fair coin. (0.304, 0.496) a 99% confidence interval of π and we conclude it is not a fair coin. (0.324, 0.486) a 99% confidence interval of π and we conclude it is not a fair coin. (0.433, 0.509) a 99% confidence interval of π and we conclude it is not a fair coin.

Q8: (This continues Q7: 2 marks) Find the P-Value of the test. Ha: π =1/2. Vs. Ha: π ≠1/2. Less than 1%. Between 1% and 2% Between 2% and 3% Between 3% and 5% Between 5% and 8%

1. Between 8% and 10%

2. Between 10% and 12%

3. Between 12% and 15%

4. Between 15% and 20%

5. Bigger than 20%.

A study of the relationship between facility conditions at gas stations and aggressiveness in the pricing of gasoline reports the accompanying data based on a sample of n = 385 stations.

Table of Observed counts

                                        Observed pricing policy

                                                 Aggressive       Neutral     Nonaggressive

                        Condition        Standard             52               73                   80

                                                Modern              58              86                  36

a. What is the expected cell count table under the null hypothesis that the facility conditions and the aggressiveness of the pricing are independent?

b. Carry out a chi-square test for the independence. What is the value of test statistic?

c. What is the reject region for the significance level 0.01? Does the data suggest that facility conditions and pricing policy are independent of one another?

A study of 20 Canadian cities finds that half of them are polluted. Six of the 20 cities are selected at random, without replacement, for closer study.

(a) What is the probability that at least 3 are polluted?

(b) What is the probability that none are polluted?

Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit . Use a significance level of 0.01 and round all values to 4 decimal places.

Advertising CostProfit

323

422

523

626

723

825

919

1025

1133

Ho: ρ = 0
Ha: ρ ≠ 0

Find the Linear Correlation Coefficient
r =

Find the p-value
p-value =   

The p-value is

Less than (or equal to) αα

Greater than αα

The p-value leads to a decision to

Do Not Reject Ho

Reject Ho

Accept Ho

The conclusion is

There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit.

There is a significant positive linear correlation between advertising expense and profit.

There is a significant linear correlation between advertising expense and profit.

There is a significant negative linear correlation between advertising expense and profit.