1. 請注意考試規則!
2. 直接在此作答，姓名: ___陳立昇________，學 號:_______03154138______
3. 另存新檔為學號
4. 記得儲存，作答完後，附件請寄至 [email protected] 與 [email protected]
5. 請記得 cc 或副本給自己
6. 從 Excel 的結果截圖重要的資訊複製貼上 Word。
7. 回答問題時請詳加說明您的虛無假設與對立假設，以及樣本（母 體）的定義為何（差異檢定時） ，根據您截圖哪裡做出什麼結論！
8. 每題請說明用到的公式是課本哪一頁哪一個公式代號。
(和 03154106 史馥慈一組)
題目開始
A. 根據所附的 Excel 資料檔，回答以下問題：
1. 這是一個從東吳大學隨機抽樣的 68 個學生所回答的問題，CC 數是 他購買搖搖杯的果汁飲料 CC 數。搖搖杯的老闆宣稱她的飲料至少 有 435CC，如果您是學校的學生代表，站在學生的立場您會如何進
行這樣宣稱的檢定？顯著水準為 0.05。
H0:μ ≥ 435 H1:μ < 435
p-value< α，有足夠證據顯示拒絕 H0 所以得出搖搖杯飲料沒有 435CC
公式:p469 Z-test statistic 𝑝̂−𝑝0
√𝑝0(1−𝑝0)
𝑛
2. 同 1，若以信賴區間 confidence interval 來估計，其上下界為何?
1
Null Hypothesis m= 435 Level of Significance 0.05
Sample Size 68
Sample Mean 432.6324
Sample Standard Deviation 6.130191
Standard Error of the Mean 0.7434
Degrees of Freedom 67
t Test Statistic -3.1849
Lower-Tail Test Calculations Area
Lower Critical Value -1.6679 For one-tailed tests:
p-Value 0.0011 TDIST value 0.001099
Reject the null hypothesis 1-TDIST value0.998901 Data
Intermediate Calculations
信賴區間介於 431.15 到 434.12 之間
公式:p392 CI for population proportion
2
Data
Sample Standard Deviation 6.130191
Sample Mean 432.6324
Sample Size 68
Confidence Level 95%
Standard Error of the Mean 0.7433948
Degrees of Freedom 67
t Value 1.9960
Interval Half Width 1.4838
Interval Lower Limit 431.15 Interval Upper Limit 434.12
Intermediate Calculations
Confidence Interval
3. 根據有無 I Phone 檢定東吳大學的學生持有愛瘋的比例為 0.5，
顯著水準為 0.05。
H0: P=0.5 H1: P≠ 0.5
p-value> α/2，沒有足夠的證據證明拒絕 H0 表示東吳大學的學生持有愛鳳的比例是 0.5
公式:p480 the steps for a Z-test for one proportions
4. 同 3，東吳大學學生持有愛瘋手機比例的信賴區間 confidence interval 為何?
3
Null Hypothesis p = 0.5 Level of Significance 0.05 Number of Items of Interest 37
Sample Size 68
Sample Proportion 0.544118
Standard Error 0.0606
Z Test Statistic 0.7276
Two-Tail Test
Lower Critical Value -1.9600 Upper Critical Value 1.9600
p-Value 0.4669
Do not reject the null hypothesis Data
Intermediate Calculations
信賴區間介於 0.4257 到 0.6625 之間
公式:p392 CI for population proportion
5. 請檢定東吳大學男學生持有愛瘋的比例是否顯著低於女生，顯著 水準為 0.5?
4
Data
Sample Size 68
Number of Successes 37
Confidence Level 95%
Sample Proportion 0.544118
Z Value -1.9600
Standard Error of the Proportion 0.0604
Interval Half Width 0.1184
Interval Lower Limit 0.4257
Interval Upper Limit 0.6625
Intermediate Calculations
Confidence Interval
令
P1: 男生持有愛鳳的比例 P2: 女生持有愛鳳的比例 H0: P1≥ P2
H1: P1< 𝑃2 d=0.5
p-value< α，有足夠證據顯示拒絕 H0
表示東吳大學男學生持有愛瘋的比例顯著低於女生
5
Hypothesized Difference 0
Level of Significance 0.5
Group 1
Number of Items of Interest 20
Sample Size 37
Group 2
Number of Items of Interest 17
Sample Size 31
Group 1 Proportion 0.540541 Group 2 Proportion 0.548387 Difference in Two Proportions -0.00785
Average Proportion 0.5441
Z Test Statistic -0.0647
Lower-Tail Test
Lower Critical Value 0.0000
p-Value 0.4742
Reject the null hypothesis Data
Intermediate Calculations
公式:p490 the steps for a Z-test for the difference in two proportions
6. 同 5，其東吳大學男女生持有愛瘋比例差距的信賴區間 confidence interval 為何?
因為 d=0.5，信賴區間為 50%，介於-0.0896 到 0.0739 之間 公式:p396 confidence interval for the difference in two population proportions
7. 如果我想檢定男生與女生所喝的搖搖杯的容量是否一樣，在顯著 水準為 0.05 下，請用信賴區間 confidence interval 的方法來說 明是否相同。必要時請說明您選擇的公式理由。
先檢定兩者的變異數是否相同 令p1 =男生的容量
p2 =女生的容量
Confidence Level 50%
Z Value -0.6745
Std. Error of the Diff. between two Proportions 0.1212
Interval Half Width 0.0818
Interval Lower Limit -0.0896
Interval Upper Limit 0.0739
Confidence Interval Confidence Interval Estimate of the Difference Between Two Proportions
Data
Intermediate Calculations
F 檢定的值趨近於 1，表示兩者的變異數相同𝜎1
= 𝜎
2 H0: p1 = p2H1: p1 ≠ p2
7
Level of Significance 0.05
Larger-Variance Sample
Sample Size 31
Sample Variance 40.44516129
Smaller-Variance Sample
Sample Size 37
Sample Variance 36.23423423
F Test Statistic 1.1162
Population 1 Sample Degrees of Freedom 30 Population 2 Sample Degrees of Freedom 36
Calculations Area
Two-Tail Test FDIST value 0.3733
Upper Critical Value 1.9862
p-Value 0.7466
Do not reject the null hypothesis Data
Intermediate Calculations
p-value> α/2，沒有足夠的證據拒絕 H0，且信賴區間位於-2.9668
7
(assumes equal population variances)
Hypothesized Difference 0
Level of Significance 0.05
Population 1 Sample
Sample Size 37 Confidence Level 95%
Sample Mean 432.6486
Sample Standard Deviation 6.019488
Population 2 Sample Degrees of Freedom 66
Sample Size 31 t Value 1.9966
Sample Mean 432.6129 Interval Half Width 3.0026
Sample Standard Deviation 6.359651
Interval Lower Limit -2.9668 Population 1 Sample Degrees of Freedom 36 Interval Upper Limit 3.0383 Population 2 Sample Degrees of Freedom 30
Total Degrees of Freedom 66
Pooled Variance 38.1483
Standard Error 1.5039
Difference in Sample Means 0.0357
t Test Statistic 0.0238
Two-Tail Test
Lower Critical Value -1.9966
Upper Critical Value 1.9966
p-Value 0.9811
Do not reject the null hypothesis Intermediate Calculations
Data Confidence Interval Estimate
for the Difference Between Two Means Data
Intermediate Calculations
Confidence Interval
到 3.0383 之間，區間包含零表示兩者無顯著差異
男生所喝的搖搖杯 CC 數的平均數和女生所喝的搖搖杯 CC 數的平均數 相同
公式:p440 pooled confidence interval for the difference between two population means
B. In the 2008 General Social Survey, participants were asked what their news source is. Among those surveyed in the 18-to 29-year-old age group, 92/262=.351 said that the Internet was their main news source. In the 50-and-over age group , o nly 59/632=.093 said that the Internet was their main news source. Use this sample information to determine a 99%
confidence interval that estimate the parameter p1-p2
=difference between population proportion who use the Internet as their main source in the two age groups.
P1= 18-to 29-year-old age group P2= 50-and-over age group
H0: P1=P2 H1: P1≠P2
99%信賴區間位於 0.1762 到 0.3394 之間，表示兩者間有顯著差異 公式:p396 confidence interval for the difference in two
B
Hypothesized Difference 0
Level of Significance 0.01
Group 1
Number of Items of Interest 92 Confidence Level 99%
Sample Size 262
Group 2
Number of Items of Interest 59 Z Value -2.5758
Sample Size 632 Std. Error of the Diff. between two Proportions 0.0317
Interval Half Width 0.0816
Group 1 Proportion 0.351145038
Group 2 Proportion 0.09335443 Interval Lower Limit 0.1762
Difference in Two Proportions 0.257790608 Interval Upper Limit 0.3394
Average Proportion 0.1689
Z Test Statistic 9.3640
Two-Tail Test
Lower Critical Value -2.5758
Upper Critical Value 2.5758
p-Value 0.0000
Reject the null hypothesis
Confidence Interval
Data Confidence Interval Estimate
of the Difference Between Two Proportions Data
Intermediate Calculations
Intermediate Calculations
population proportions
p490 the steps for a Z-test for the difference in two proportions
C. B. A random sample of five college women was asked for their own heights and their mothers’ heights. The researchers wanted to know whether college women are taller on average than their mothers. The results (inches) follow:
Pair 1 2 3 4 5 Daughter 66 64 64 69 66 Mother 61 62 65 66 62
Find the 95% confidence interval for the parameter of interest in this situation.
μm:
mothers’ heightsμd:
college women’s heights H0: μm = μdH1: μm ≠ μd
信賴區間介於 62.77 到 66.23 之間 公式:p392
D. Following are data for 20 individuals on resting pulse rate and whether or not the individual regularly exercise.
Person 1 2 3 4 5 6 7 8 9 10
C
Data
Sample Standard Deviation 2.4152295
Sample Mean 64.5
Sample Size 10
Confidence Level 95%
Standard Error of the Mean 0.763762616
Degrees of Freedom 9
t Value 2.2622
Interval Half Width 1.7278
Interval Lower Limit 62.77 Interval Upper Limit 66.23
Intermediate Calculations
Confidence Interval
Pulse 72 62 72 84 60 63 66 72 75 64 Regularly Exercise N Y Y N Y Y N N Y Y
Person 11 12 13 14 15 16 17 18 19 20 Pulse 62 84 76 60 52 60 64 80 60 64
Regularly Exercise N N N Y Y N Y Y N Y Calculate a 95% confidence interval for the difference in means for the two groups.
F 檢定值趨近於 1，表示兩者的母體變異數相同 令
P1:無規律運動者 P2:有規律運動者 H0:P1-P2≠0 H1:P1-P2=0
D
Level of Significance 0.05
Larger-Variance Sample
Sample Size 9
Sample Variance 89
Smaller-Variance Sample
Sample Size 11
Sample Variance 60.89090909
F Test Statistic 1.4616
Population 1 Sample Degrees of Freedom 8 Population 2 Sample Degrees of Freedom 10
Calculations Area
Two-Tail Test FDIST value 0.2817
Upper Critical Value 3.8549
p-Value 0.5635
Do not reject the null hypothesis Data
Intermediate Calculations
D
(assumes equal population variances)
Data Confidence Interval Estimate
Hypothesized Difference 0
for the Difference Between Two Means
Level of Significance 0.05
Population 1 Sample Data
Sample Size 9 Confidence Level 95%
Sample Mean 70.6667
Sample Standard Deviation 9.43398 Intermediate Calculations
Population 2 Sample Degrees of Freedom 18
Sample Size 11 t Value 2.1009
Sample Mean 65.0909 Interval Half Width 8.0892
Sample Standard Deviation 7.80326
Confidence Interval
Intermediate Calculations Interval Lower Limit -2.5135
Population 2 Sample Degrees of Freedom 10
Total Degrees of Freedom 18
Pooled Variance 73.3838
Standard Error 3.8503
Difference in Sample Means 5.5758
t Test Statistic 1.4481
Two-Tail Test
Lower Critical Value -2.1009
Upper Critical Value 2.1009
p-Value 0.1648
Do not reject the null hypothesis
p-value< α
信賴區間介於-2.5135 到 13.6650 之間，表示無顯著差異
公式:p440 pooled confidence interval for the difference between two population means
8. Extra point. 請檢定上題 7 男女生的手搖杯 CC 數變異數是否相 等，顯著水準為 0.05。
Ｆ檢定值趨近於 1，表示兩者變異數相同
8
Level of Significance 0.05
Larger-Variance Sample
Sample Size 31
Sample Variance 40.4451613
Smaller-Variance Sample
Sample Size 37
Sample Variance 36.2342342
F Test Statistic 1.1162
Population 1 Sample Degrees of Freedom 30 Population 2 Sample Degrees of Freedom 36
Calculations Area
Two-Tail Test FDIST value 0.3733
Upper Critical Value 1.9862
p-Value 0.7466
Do not reject the null hypothesis Data
Intermediate Calculations
這次期中考，其實我並沒有準備的很好。考試前想說是用電腦作 答，而 PHstat 又是平常作業都會用到的，就沒有特別去複習，對於 不同題目該選擇的公式和作法也就沒有弄得很清楚。結果考試時看到 題目就忘了針對那個題目的解法，也忘記應該使用的公式為何，因此 錯了好幾題。我會將 PHstat 的用法好好的熟悉，之後的考試會提早 複習，也把課本中的那些公式弄清楚，哪一種題目應該使用哪一個公 式，還有像 pooled 和 unpooled 的區分也要熟悉。希望在下一次的考 試能有所改善。
