mathematics

Questions from Mario F. Triola Elementary Statistics.
8.4.20
Testing Hypotheses. Use critical value method or p-value method for testing hypotheses. Identify the null and alternative hypothesis, test statistics, p-value (or range of p-values), critical value(s) and  state the final conclusion that addresses the original claim.

Question
Ages of Race: Car Drivers Listed below are the ages (years) of randomly selected race car drivers (based on data reported in USA Today). Use a 0.05 significance level to test the claim that the mean age of all race car drivers is greater than 30 years.
32 32 33 33 41 29 38 32 33 23 27 45 52 29 25
9.2.18 (Inferences of two samples)
Marathon Finishers: In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also, 12, 883 women finished and 163 dropped out (based on data from the New York Times). We want to use a 0.01 significance level to test the claim that the rate of those who finish is the same for men and women.
a. Test the claim using a hypotheses test
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, do men and women finish the New York City at the same rate?
x
y

10.3.10(Correlation and Regression).
Finding the Equation of the Regression Line. Use the given data to find the equation of the
regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by
the regression line.
10
8
13
9
11
14
6
4
12
7
5
7.46
6.77
12.74
7.11
7.81
8.84
6.08
5.39
8.1 6.4 5.7
5
2
3

11.2.12 (Goodness –of-Fit)
Conduct hypotheses test and provide the statistics, critical value, and/ or P-value, and state the
conclusion

Question;
Births: Records of randomly selected births were obtained and categorized according to the day
of the week that they occurred ( based on data from national Center for health Statistics).
Because babies are unfamiliar with our schedule of weekdays, a reasonable claim is that births
occur on the different days with equal frequency. See the table below and use 0.01 significance
level to test that claim. Can you provide an explanation for the result?
Day
Sun
Mon
Tues
Wed
Thurs
Fri
Sat
Number
77
110
124
122
120
123
97
of Births
12.3.10 (Analyses of Variance)
Pulse rate: The following table lists pulse rates obtained from Data set 1 appendix B. Use 0.05
significance level and apply the methods of two-way analysis of varience. What do you conclude?
Under 30 years of Age
Over 30 Years of Age
Female
78,
76,76,72,66,72,78,62,72,74,56
104,78,64,60,98,82,98,90,96
Male
60,80,56,68,68,74,74,68,62,56
46,70,62,66,90,80,60,58,64,60

Question and Answer

1. An engineer is going to redesign an ejection seat from an airplane. The seat was designed for pilots weighing between 150lb and 201lb. The new population of pilots has normally distributed weights with a mean of 156lb and a standard deviation of 33.7lb.
If a pilot is randomly selected, find the probability that his weight is between 150lb and 201lb
2. Assume that women’s heights are normally distributed with a mean given by, µ = 62.1 in, and a standard deviation given by Ō = 2.8 in,.
a. If 1 woman is randomly selected, find the probability that her heights is less than 63 in,
b. If 33 women are randomly selected, find the probability that they have a mean heights less than 63 in, (a) The probability is approximately what?

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