Hypothesis Testing Please answer as soon as possible Show your steps and follow
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Hypothesis Testing
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For each of the following problems, set up and perform the required hypothesis test. If the level of significance is not indicated, use ? = 0.05.
1. Researchers want to test the claim that there are more births in September than January. They collected data on the number of births at a local hospital for one week each in September 2017 and January 2018, given in the table below. Note that it is well-known that the number of hospital births is dependent on the day of the week, with fewer births on weekend days. Use a 0.05 significance level to test the claim that there are more births in September than in January. You may assume that all populations involved are normally distributed.
2. Customer waiting times are known to be normally distributed. Two different line methods are studied at the Humber Valley Credit Union. When 25 randomly selected customers enter any one of the 3 available waiting lines, their wait times had a mean of 6.896 minutes and standard deviation of 3.619 minutes. When 20 randomly selected customers enter a single main line that feeds the 3 individual teller stations, their waiting times have a mean 7.460 minutes and a standard deviation of 1.841 minutes. Test the claim that the single line method is less variable, ? = 0.01.
Mon Tue Wed Thurs Fri Sat Sun September 2017: 19 16 11 11 22 5 8 January 2018: 20 13 9 10 20 4 4Explanation / Answer
Result:
1. Researchers want to test the claim that there are more births in September than January. They collected data on the number of births at a local hospital for one week each in September 2017 and January 2018, given in the table below. Note that it is well-known that the number of hospital births is dependent on the day of the week, with fewer births on weekend days. Use a 0.05 significance level to test the claim that there are more births in September than in January. You may assume that all populations involved are normally distributed.
Mon
Tue
Wed
Thurs
Fri
Sat
Sun
September 2017:
19
16
11
11
22
5
8
January 2018:
20
13
9
10
20
4
4
This is upper tail test
R code:
# test
sep <- c(19,16,11,11,22,5,8)
jan <- c(20,13,9,10,20,4,4)
t.test(sep,jan,alternative = "g", var.equal = TRUE, conf.level=.95)
R output:
Two Sample t-test
data: sep and jan
t = 0.5016, df = 12, p-value = 0.3125
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
-4.376934 Inf
sample estimates:
mean of x mean of y
13.14286 11.42857
Calculated t=0.5016, P=0.3125 which is > 0.05 level.
Ho is not rejected.
There is not enough evidence to support the claim that there are more births in September than in January.
2. Customer waiting times are known to be normally distributed. Two different line methods are studied at the Humber Valley Credit Union. When 25 randomly selected customers enter any one of the 3 available waiting lines, their wait times had a mean of 6.896 minutes and standard deviation of 3.619 minutes. When 20 randomly selected customers enter a single main line that feeds the 3 individual teller stations, their waiting times have a mean 7.460 minutes and a standard deviation of 1.841 minutes. Test the claim that the single line method is less variable, ? = 0.01.
s1=3.619
> s2=1.841
> f=s1^2/s2^2;f
[1] 3.864289
Calculated F=3.8643 is > critical F(24,20) at 0.01 level = 2.859
Ho is rejected.
There is enough evidence to support the claim that the single line method is less variable.
Mon
Tue
Wed
Thurs
Fri
Sat
Sun
September 2017:
19
16
11
11
22
5
8
January 2018:
20
13
9
10
20
4
4
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