Hi Q1. You ordered 20 computer chips from a manufacturer. We know that 5% of the

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Hi

Q1. You ordered 20 computer chips from a manufacturer. We know that 5% of the chips coming out of the production line are defective. Let X be the number of defective chips among the
20 that you will receive.
What is the probability that 2 or more chips among the 20 will be defective?
Help:You can use a statistical software or Excel to answer this question. Or, you can use your the formula for binomial probabilities .
A. .365
B. .264
C. .102
D. .450

Q2. In a hypothesis test statisticians set up two hypotheses: the null and the alternative (research) hypothesis.
Suppose that in a study the null hypothesis has been rejected at 1% significance level. What would have been the result of this test if the significance level had been 5% (the same test using the same sample)?
A. The null hypothesis would have been rejected at 5% significance level.
B. The null hypothesis would have been accepted at 5% significance level.
C. It is impossible to tell based on the given information
D. It depends whether it is a two-sided or one-sided test

Q3. To help your restaurant marketing campaign target the right age levels, you want to find out whether there is a statistically significant difference between the average age of your customers (), and the average age of the general population in town which is 43.1 years.
The null hypothesis is that u=43.1 and the alternative hypothesis is that u <>43.1.
Based of a random sample a 95% confidence interval for the unknown is given as (40.5, 42.6).
What would be your decision in the hypothesis test at 5% significance level?

A. One would need to know the t statistics in order to answer this question
B. It is impossible to tell based only on the confidence interval
C. Accept null hypothesis at 5% significance level.
D. Reject the null hypothesis at 5% significance level.

Q4. What is the interpretation of R2 in a multuple linear regression analysis?

A. It represents the proportion of the total variation of the response explained by the linear regression model.
B. It represents the proportion of the total variation of the predictors explained by the linear regression model.

C. It represents the relationship between two predictor variables in a linear regression model.
D. It represents the non-linear relationship between two predictor variables in a linear regression model.

Q5. In a simple linear regression model the “p-value” corresponding to the slope is 0.45. What implication can you draw from this?
A. The slope of the regression line is significantly different from zero at 5% significance level.
B. The slope of the regression line is not significantly different from zero at 5% significance level.
C. The variances of the error terms are unequal.
D. The error terms do not follow normal distribution.

Q6. What does the correlation coefficient between two variables measure?
A. The strength of the linear relationship between two variables.
B. The strength of the non-linear relationship between two variables.
C. The difference of the sample variances
D. The strength of the quadratic relationship between the two variables

Q7. Suppose that the correlation coefficient between two variables is very close to zero. Does this imply that there is very little relationship between the two variables?
A. Yes
B. No, there may be a strong non-linear relationship
C. Yes, if the distributions of the two variables are mound shaped and symmetric
D. Yes, if the distributions of the two variables are similar

Q8. On the same data set we run both lineat regression and LASSO. In both cases we denote by Yi the fitted values.

The Residual Sum of Squares is calculated in both cases as E(Yi - Yi)2 . Which of the following statements is correct?

A. The Residual Sum of Squares in the LASSO model can not be larger than the Residual Sum of Square in the linear regression model

B. The Residual Sum of Squares in the linear regression model can not be larger than the Residual Sum of Square in the Lasso model

C. The Residual Sum of Squares in the linear regression model is exactly the same as the Residual Sum of Square in the Lasso model

D. The Residual Sum of Squares in the linear regression model is very close to the Residual Sum of Square in the Lasso model

Explanation / Answer

1) X~ Binomial (20, 0.005)

P(X>=2) = 1 - P(X<2)

=> 1 - { P(X=0) + P(X=) }

Using the formula P(X= r) = nCr x pr x (1-p)n-r

We get P(X>=2) = 0.00450 => 0.450%

Hence, option D

2) The significance level, also denoted as alpha or , is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

So, we need more surety at 1% significance than at 5% significance..Thus if a test is rejected at 1% , it is not necessary it eill be rejected at at 5% significant level but a test rejected at 5% will be rejected at 1% also.So, the null hypothesis would have been accepted at 5% significant level.

Hence, option B

NOTE - We are bound to give answer to 1 question only. i have already Answered 2 questions. Please post the next questions as separate questions. Thanks!

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