## Description

**Math 227-Honor Section Last name, First name:________________,____________**

Ask at least 70 female and 70 male students the following 5 questions: ______________/10 pts.

- What is your age?
- What is your GPA?
- Are you going to transfer to a university?
- How many hours a week they study for their course?

Here are the example of the collecting data:

# of Female student | Age | GPA | Transfer | # of hour |

1 | 23 | 3.3 | Yes | 10 |

2 | 19 | 3.6 | No | 5 |

3 | 24 | 1.7 | Yes | 6 |

# of Male student | Age | GPA | Transfer | # of hour |

1 | 22 | 3.1 | Yes | 7 |

2 | 27 | 2.8 | yes | 4 |

3 | 25 | 2.0 | no | 9 |

(Attention: Keep your data for the next project)

**From age data for both groups, find:**

- The average.
- The median.
- The standard deviation
- The variance.
- The range of usual.
- The acceptable range
- The percentile of the age of 20.
- Find P47
- Find the 5 number summary.
- Construct the boxplot
- Find outlier(s) if any
- Construct the steam and leaf plot.
- Construct the frequency table with at least 4 class width.
- Construct the histogram.
- Construct pie chart.
- Construct Frequency Polygon.
- Construct Ogive.
- How many percent (probability) of students (including female and female students) are going to transfer?
- Find the probability of students who are going to transfer.
- Find the probability of students who are not going to transfer.
- Find the probability of selecting a student who is a female or is going to transfer.
- At a 0.05 significance level test the claim that the average GPA of LACC students (including female and male) is less than 3.0.
- At a 0.05 significance level, can you reject the claim that more than 70% of LACC students is going to transfer to a university?
- Construct a 95% confidence interval estimate of the average GPA of LACC students.
- How many college students must be randomly selected to estimate the mean GPA of college students in LACC? We want 99% confidence that the sample mean is within 0.3 points of the population mean, and the population standard deviation is 0.5.
- a) At a significance level, test the claim that the LACC female student’s average GPA is greater than the LACC male students’ average GPA.
- a) At a significance level, test the claim that the percent of transferring to a university is the same for both female and male students.

**From # of studying hour for both female and male students:**

18. Find the range of usual

**From the Transfer data: **

b) Construct the 95% significant difference between the two means.

b) Construct the 95% significant different between the two proportions.

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## Explanation & Answer

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Question (22.) At a 0.05 significance level test the claim that the average GPA of LACC

students (including female and male) is less than 3.0.

Formulate the Null and Alternative Hypotheses

H 0 : 3.0 ; The average GPA of LACC students (including female and male) is 3.0

H1 : 3.0 ; The average GPA of LACC students (including female and male) is less than 3.0

In evaluating the claim, a right-tail test is appropriate since it is a one-directional statement that

could be rejected by an extreme result in one direction direction. The center of the hypothesized

distribution of sample means for samples of n 140 will be 3.14.

Select the Significance Level

For this test, we will use the 0.05 level of significance. The sum of the one tail areas will be 0.05.

Select the Test Statistic and Calculate Its Value

x 0

The test statistic is t

, and the t distribution will be used to describe the sampling

s

n

distribution of the mean for samples of n 140 . The center of the distribution is 3.14 , which

corresponds to t 0.0000 .Since the population standard deviation is unknown, s is used to

estimate. The sampling distribution has an estimated standard error of

s

n

0.542

140

0.046

and the calculated value of t will be

t

x 3.14 3.0

3.04

s

0.046

n

Identify the Critical Value for the Test Statistic and State the Decision Rule

For this test, has been specified as 0.05. The number of degrees of freedom is

df 140 1 130 . The t distribution table is now used in finding the value of t that corresponds

to a one-tail area of 0.01 and139 degrees of freedom. We find this critical value to be

t c 1.656 .Since it is observed that t 3.04 t c 1.656 , it is then concluded that the null

hypothesis is not rejected.

Conclusion:

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough

evidence to claim that the population mean μ is less than 3.0, at the 0.05 significance level.

Question (23.) At a 0.05 significance level, can you reject the claim that more than 70% of

LACC students is going to transfer to a university?

The following information is provided: The sample size is N=140, the number of favorable cases

is X=47, and the sample proportion is p¯= 37 / 140 0.3357 , and the significance level is α=0.05

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0 : p 0

H1 : p 0

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to

be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a

right-t...