Posted: December 21st, 2022
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STAT 200: Introduction to Statistics
Homework #5: Lesson 8, Sections 15 through Lesson 9, Sections 12
1. (2 points) A claim is made that when parents use the XSORT method of gender selection during invitro fertilization, the proportion of baby girls is greater than 0.5. The latest results show that among 945 babies born to couples using the XSORT method of gender selection, 879 were girls.
a. (1 point) Express the original claim in symbolic form.
b. (1 point) Identify the null and alternative hypothesis.
2. (10 points) A 0.05 significance level is used for a hypothesis test of the claim that when parents use the XSORT method of gender selection, the proportion of baby girls is different from 0.5. Assume that the data consists of 55 girls born in 100 births, so the sample statistic of 0.55 results in a zscore that is 1.00 standard deviation above 0.
a. (1 point) Identify the null and alternative hypothesis.
b. (1 point) What is the value of α?
c. (1 point) What is the sampling distribution of the sample statistic?
d. (1 point) Is this a twotailed, lefttailed, or righttailed test? Why?
e. (1 point) What is the value of the test statistic?
f. (2 points) What is the Pvalue?
g. (1 point) What is the critical value?
h. (1 point) What is the area of the critical region?
i. (1 point) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why?
3. (8 points) The data set below contains data from a simple random sample of 100 M&Ms, 8 of which are brown (i.e. 8% or the proportion of 8 out of 100 are brown). Use a 0.05 significance level to test the claim of the Mars Candy Company that the percentage of brown M&Ms is equal to 13%.
Count 
Red 
Orange 
Yellow 
Brown 
Blue 
Green 
1 
0.751 
0.735 
0.883 
0.696 
0.881 
0.925 
2 
0.841 
0.895 
0.769 
0.876 
0.863 
0.914 
3 
0.856 
0.865 
0.859 
0.855 
0.775 
0.881 
4 
0.799 
0.864 
0.784 
0.806 
0.854 
0.865 
5 
0.966 
0.852 
0.824 
0.840 
0.810 
0.865 
6 
0.859 
0.866 
0.858 
0.868 
0.858 
1.015 
7 
0.857 
0.859 
0.848 
0.859 
0.818 
0.876 
8 
0.942 
0.838 
0.851 
0.982 
0.868 
0.809 
9 
0.873 
0.863 


0.803 
0.865 
10 
0.809 
0.888 


0.932 
0.848 
11 
0.890 
0.925 


0.842 
0.940 
12 
0.878 
0.793 


0.832 
0.833 
13 
0.905 
0.977 


0.807 
0.845 
14 

0.850 


0.841 
0.852 
15 

0.830 


0.932 
0.778 
16 

0.856 


0.833 
0.814 
17 

0.842 


0.881 
0.791 
18 

0.778 


0.818 
0.810 
19 

0.786 


0.864 
0.881 
20 

0.853 


0.825 

21 

0.864 


0.855 

22 

0.873 


0.942 

23 

0.880 


0.825 

24 

0.882 


0.869 

25 

0.931 


0.912 

26 




0.887 

27 




0.886 

a. (1 point) Identify the null and alternative hypothesis.
b. (1 point) Is this a twotailed, lefttailed, or righttailed test? Why?
c. (1 point) What is the value of the test statistic?
d. (2 points) What is the Pvalue?
e. (1 point) What is the critical value?
f. (1 point) What is the area of the critical region?
g. (1 point) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why did you respond with this answer, and what does it mean?
4. (10 points) The data set in problem 3 presents a sample of 100 plain M&M candies that randomly selected (without replacement) from a bag which contained a total of 465 M&M candies. The weight of each M&M (in grams) is recorded in the table above and in the available Excel Data Set file. From this simple random sample, there were 19 green M&Ms with a mean of 0.8635 g and a standard deviation of 0.0570. Use a 0.05 significance level to test the claim that the mean weight of all M&Ms is equal to 0.8535, which is the mean weight required so that M&Ms have the weight printed on the packaged label.
a. (1 point) Identify the null and alternative hypothesis.
b. (1 point) Is this a twotailed, lefttailed, or righttailed test? Why?
c. (2 points) What is the value of the test statistic?
d. (2 points) What is the Pvalue?
e. (1 point) What is the critical value?
f. (1 point) What is the area of the critical region?
g. (1 point) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why did you respond with this answer, and what does it mean?
h. (1 point) Do green M&Ms appear to have weights consistent with the package label?
5. (10 points) The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Listed below (and in the Excel Data File) are the IQ scores of randomly selected professional pilots. It is claimed that because the professional pilots are a more homogenous group than the general population (i.e. they are “more alike” than a random group of people), they have IQ scores with a standard deviation less than 15. Test the claim using a 0.05 significance level.
121 
116 
115 
121 
116 
107 
127 
98 
116 
101 
130 
114 
a. (1 point) Identify the null and alternative hypothesis.
b. (1 point) Is this a twotailed, lefttailed, or righttailed test? Why?
c. (2 points) What is the value of the test statistic?
d. (2 points) What is the critical value?
e. (2 points) What is the Pvalue?
f. (1 point) What is the area of the critical region?
g. (1 point) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why did you respond with this answer, and what does it mean?
6. (10 points) Listed below (and in the available Excel Data Set file) are the PSAT and SAT scores from prospective college applicants. The scores were reported by subjects who responded to a request posted by the web site talk.collegconfidential.com. There is a claim that higher PSAT scores correlate to higher SAT scores. Use this data set to argue for or against that claim.
PSAT 
183 
207 
167 
206 
197 
142 
193 
176 
SAT 
2200 
2040 
1890 
2380 
2290 
2070 
2370 
1980 
a. (1 point) Identify the null and alternative hypothesis.
b. (1 point) Is this a twotailed, lefttailed, or righttailed test? Why?
c. (2 points) What is the value of the test statistic?
d. (2 points) What is the critical value?
e. (2 points) What is the Pvalue?
f. (1 point) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why did you respond with this answer, and what does it mean?
g. (1 point) Is there anything about the data that might make the results questionable?
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