Statistics and Probability Answers

A passenger arrives at a bus stop at 10 am knowing that bus will arrive at random time between 10 am and 10:30 am. What is the probability that he will have to wait lower than 10 minutes?If the bus has not arrived until 10 : 15 am, what is the probability that he will have to wait another 10 minutes?

Expert's answer

According to a study done last year, the average monthly expenses for mobile phone loads of college students in San Mateo, Rizal was P 400.00. A statistics student believes that this amount has decreased since January of this year. Is there a reason to believe that this amount has decreased if a random sample of 50 students has an average monthly expense for mobile phone loads of P 380.00? Use .05 level of significance. Assume the population standard deviation is P 75.00.  

Step 1: State the null and alternative hypotheses.

(1.) Null Hypothesis (Ho):

(2.) Alternative Hypothesis(Ha):

(3.) Write Ho in words:

(4.) Write Ha in words:

Step 2: Level of significance and the Type of test.

(5.) Level of Significance: α =

(6.) Two-tailed Test or One-tailed Test

Step 3: Compute the test statistic.

(7.) = (8.)  = ______ (9.) ẟ = ______ (10.) n = _or   s =

ComputationEncircle the formula to be used

4: Determine the critical value.

According to a study done last year, the average monthly expenses for mobile phone loads of college students in San Mateo, Rizal was P 400.00. A statistics student believes that this amount has decreased since January of this year. Is there a reason to believe that this amount has decreased if a random sample of 50 students has an average monthly expense for mobile phone loads of P 380.00? Use .05 level of significance. Assume the population standard deviation is P 75.00.  

Which of the following is false about the central limit theorem (CLT)?

a.As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.

b.If we take more samples from the original population, the sampling distribution is more likely to be nearly normal.

c.The CLT states that the sampling distribution will be centered at the true population parameter.

d.If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size.

Students are asked to count the number of chocolate chips in 22 cookies for a class activity. They found that the cookies on average had 14.77 chocolate chips with a standard deviation of 4.37 chocolate chips. After collecting the data, a student reports the standard error of the mean to be 0.93 chocolate chips. What is the best way to interpret the student’s result?

a.0.93 chocolate chips is a measure of the variability we’d expect in calculations of the mean number of chocolate chips if we took repeated random samples of 22 cookies.

b.0.93 chocolate chips is a measure of the variability in the mean number of chocolate chips across all chocolate chip cookies.

c.0.93 is the standard deviation of the number of chocolate chips in a chocolate chip cookie.

d.The student either made a calculation error or his result is meaningless, because it does not make sense to talk about 0.93 chocolate chips.

Two card are drawn from a deck. How many possible values can each of the following variables take?

1. Sum of the numbers on the card

2. Number of times both cards are black

3. Number of times both cards 7s

4. Number of times the first card is six and the second card is red

 In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses resulted in a mean of 96,700 miles and a standard deviation of 37,500 miles. At the 0.05 level of signıficance, test the manufacturer's claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

1. Claim:

Ho:

Ha:

2. Level of Significance:

Test- statistic:

Tails in Distribution:

3. Reject Ho if:

4. Compute for the value of the test statistics.

5. Make a decision:

6. State the conclusion in terms of the original problem.

A. Construct a scatterplot of the following bivariate data:

1. 

Age of person, in years  | 11 | 12 | 13 | 14 | 15 |

Weight (kg)            | 40 | 42 | 38 | 45 | 51 |   

2. 

Age of car, in years   | 11 | 12 | 13 | 14 | 15 | 

Mileage, in km/liter   | 40 | 42 | 38 | 45 | 51 | 

B. Identify the dependent and independent variable in each of the following pairs of variables. Write your answer on the space provided

1. The base and the area of the triangle.

Independent Variable:

Dependent Variable:

2. Cost and age of car.

Independent Variable:

Dependent Variable:

3. The age and birth date.

Independent Variable:

Dependent Variable

B. Survey tests on seIf-concept and on leadership skill were administered to student-leaders. Both tests use a 10-point Likert scale with 10 indicating the highest scores for each test. Scores for students on the tests follow:

Student    | A   |  B   |  C  |  D  | E   |  F  |  G | 

Self

-Concept  | 7.1 | 5.6 | 6.8 | 7.8 | 8.3 | 5.4 | 6.3 |

Leader   | 3.4 | 6.0 | 7.8 | 8.8 | 7.0 | 6.5 | 8.3 |

-ship Skill

1. Compute the coeficient of correlation r.

2. Interpret the results in terms of strength and direction of correlation.

3. Find the regression line that will predict the leadership skill if the self-concept score is known.

B. Survey tests on seIf-concept and on leadership skill were administered to student-leaders. Both tests use a 10-point Likert scale with 10 indicating the highest scores for each test. Scores for students on the tests follow:

Student    | A   |  B   |  C  |  D  | E   |  F  |  G | 

Self

-Concept  | 7.1 | 5.6 | 6.8 | 7.8 | 8.3 | 5.4 | 6.3 |

Leader     | 3.4 | 6.0 | 7.8 | 8.8 | 7.0 | 6.5 | 8.3 |

-ship Skill

1. Compute the coeficient of correlation r.

2. Interpret the results in terms of strength and direction of correlation.

3. Find the regression line that will predict the leadership skill if the self-concept score is known.