Assign a number (01, 02, . . . , 05) to each member in your group and use Table
ID: 3154879 • Letter: A
Question
Assign a number (01, 02, . . . , 05) to each member in your group and use Table A to choose a data set from Exercises 7.26, 7.30, 7.31, 7.40, and 7.135 (two students cannot get the same data).
1. Explain how your data set was choosen from the above data sets, and answer the following.
(a) Create a histogram or a stemplot, a boxplot, and a Normal quantile plot of the data. Write a careful description of the distribution. Make sure to note any outliers, and comment on the skewness and Normality of the data.
(b) Based on your observations in part (a), is it appropriate to analyze these data using the t procedures? Briefly explain your response.
(c) Find the mean, the standard deviation, and the standard error of the mean for this sample.
(d) Calculate the 90% confidence interval for the population mean with the margin of error. Write a short summary describing the meaning of the confidence interval in context.
2. A high-school teacher in a low-income urban school in Worcester, Massachusetts, used cash incentives to encourage student learning in his AP statistics class. In 2010, 15 of the 61 students enrolled in his class scored a 5 on the AP statistics exam. Worldwide, the proportion of students who scored a 5 in 2010 was 0.15. Is this evidence that the proportion of students who would score a 5 on the AP statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15? State hypotheses, find the P-value, and give your conclusions in the context of the problem. Does this study provide actual evidence that cash incentives cause an increase in the proportion of 5’s on the AP statistics exam? Explain your answer
Explanation / Answer
2.
Z-Test For Proportion
Set Up Hypothesis
Null, the proportion of students who scored a 5 in 2010 was 0.15. H0:P=0.15
Alternate,the proportion of students who scored a 5 in 2010 was higher than 0.15. H1: P>0.15
Test Statistic
No. Of Success chances Observed (x)=15
Number of objects in a sample provided(n)=61
No. Of Success Rate ( P )= x/n = 0.2459
Success Probability ( Po )=0.15
Failure Probability ( Qo) = 0.85
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.2459-0.15/(Sqrt(0.1275)/61)
Zo =2.0977
| Zo | =2.0977
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.098 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.09766 ) = 0.01797
Hence Value of P0.05 > 0.01797,Here we Reject Ho
ans: we have an evidence that cash incentives cause an increase in the proportion of 5’s on the AP statistics exam
1.
c.
mean:7.281
standard diviation 0.0963
morgin of error
Margin of Error = Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
Mean(x)=7.281
Standard deviation( sd )=0.0963
Sample Size(n)=5
Margin of Error = Z a/2 * 0.0963/ Sqrt ( 5)
= 1.64 * (0.043)
= 0.071
d.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=7.281
Standard deviation( sd )=0.0963
Sample Size(n)=5
d.
Confidence Interval = [ 7.281 ± Z a/2 ( 0.0963/ Sqrt ( 5) ) ]
= [ 7.281 - 1.64 * (0.043) , 7.281 + 1.64 * (0.043) ]
= [ 7.21,7.352 ]
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