7 Intro to Statistics Problems

Question 1 (15 points)

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher.

Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0.

If you conducted a hypothesis test the null and alternative hypotheses would be:

Note: x ¯  is the sample average, typically refered to has xbar, an x with a horizintal line over it.

Question 1 options:

	A. Ho: x ¯= 4.75,        Ha: x ¯ > 4.75
	B. Ho: μ ≥ 4.5,            Ha: μ < 4.5
	C. Ho: μ = 4.75,          Ha: μ > 4.75
	D. Ho: μ = 4.5,            Ha: μ > 4.5

 

Question 2 (15 points)

 

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone.
The organization thinks that, currently, the mean is higher.

Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone.
The sample mean was 4.75 hours with a sample standard deviation of 2.0.

If you conducted a hypothesis test and made a Type 1 error what would that error be: 

Question 2 options:

	A. To conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher.
	B. To conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
	C. To conclude that the mean hours per week currently is 4.5, when in fact, it is higher.
	D. To conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher.

 

Question 3 (15 points)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees.

Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2.

Do the data support your claim at the 1% level?

What is the null and alternate hypothesis for this hypothesis test?

Note: x ¯  is the sample average, typically refered to has xbar, an x with a horizintal line over it.

 

Question 3 options:

	A. Ho: x ¯= 4.5,        Ha: x ¯> 4.5
	B. Ho: μ ≥ 4.5,          Ha: μ < 4.5
	C. Ho: μ = 4.75,        Ha: μ > 4.75
	D. Ho: μ = 4.5,          Ha: μ > 4.5

 

Question 4 (15 points)

 

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees.

Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2.

Do the data support your claim at the 1% level?

What is the significance level of the test?

Enter answer as percent without the percent sign to zero decimal places without the decimal point or as a 2 place decimal.

What is the appropriate distribution for performing this test?

a.     z distribution

b.     t distribution

c.     either distribution

d.     neither.  This question does not depend on knowing the appropriate distribution.

Select and enter the appropriate letter.

What is the critical value for the test statistic?

Enter answer as a 3 place decimal (rounded to 3 decimal places as necessary)

What is the numerical value of the test statistic?

Enter answer as a 1 place decimal (rounded to 1 decimal place as necessary)

What is your decision based upon performing the Hypothesis test?

a.     There is insufficient evidence, based upon the data, to accept the alternate hypothesis.

b.     There is sufficient evidence, based upon the data, to accept the alternate hypothesis.

c.     It is not possible to make a decision (null or alternate), based upon the data.

d.     Either decision is possible based upon the data obtained in performing this hypothesis test.

Select and enter the appropriate letter.

 

Question 5 (15 points)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees.

Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 4.8 with a sample standard deviation of 1.2.

Do the data support your claim at the 1% level?

Pvalue approach

What is the Pvalue Decision Rule?

a.     The data supports the alternate hypothesis if the Pvalue is greater than the significant level of the test.

b.     The data supports the alternate hypothesis if the Pvalue is less than the significant level of the test.

c.     The Pvalue must equal the significant level of the test for the decision of the hypothesis test to be alternate.

d.     The Pvalue must not be equal the significant level of the test for the decision of the hypothesis test to be alternate.

Select the correct answer and enter the appropriate letter.

 

What is the Pvalue for this hypothesis test?

Enter answer as a percent rounded to 0 decimal places without the percent sign or as a decimal rounded to 2 decimal places.

 

What is your decision based upon performing the Hypothesis test?

a.     There is insufficient evidence, based upon the data, to accept the alternate hypothesis.

b.     There is sufficient evidence, based upon the data, to accept the alternate hypothesis.

c.     It is not possible to make a decision (null or alternate), based upon the data obtained in performing this hypothesis test.

d.     Either decision is possible, null or alternate hypothesis, based upon the data obtained in performing this hypothesis test.

Select and enter the appropriate letter.

 

 

Question 6 (15 points)

A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective.

She takes four new students and records their 18-hole scores before learning the new technique and then after
having taken her class.  She then conducts a hypothesis test at a significance level of 5%.

The data are as follows.

 

	Player 1	Player 2	Player 3	Player 4
Mean score before class	83	78	93	87
Mean score after class	80	80	86	86

 

What is the Null Hypotheses?

a.     The mean scores before the class and the mean scores after the class are the same.

b.     The mean scores before the class are greater than the mean scores after the  class. 

Enter your answer by the appropriate identifying letter.

 

What is the Alternate Hypothesis?

a.     The mean scores before the class and the mean scores after the class are the same.

b.     The mean scores before the class are greater than the mean scores after the  class.

Enter your answer by the appropriate identifying letter.

 

What is the significance level of the test?

Enter answer as a percent without the percent sign to 0 decimal places or as a decimal to 2 decimal places.

 

What is the appropriate distribution for performing this test?

a.     z distribution

b.     t distribution

c.     Neither of the above distributions

d.     Either of the above distributions

Enter your answer by the appropriate identifying letter.

 

What is the critical value?

Enter answer rounded to 3 place accuracy.

 

What is the numerical value of the test statistic?

Enter answer as decimal rounded to 2 decimal places.

 

What is your decision?

a.     Reject the null hypothesis

b.     Do not reject the null hypothesis

Enter your answer by the appropriate identifying letter.

 

What is the Pvalue for this hypothesis test.

Enter answer as a percent without the percent sign with 0 decimal places or as a decimal rounded to 2 decimal places.

 

 

Question 7 (15 points)

Use the following 4 x, y pairs to find the equation of the least squares regression line.

x	2	3	5	6
y	5	9	10	12

Round the first answer (constant) to 0 decimal places and the second answer (slope) to 1 decimal place.

 

 

Based on the above equation, what is the predicted value of y if x = 10? 
Round answer to 0 decimal places.

 

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