3. A human society claims that less than 35% of households own a dog or a cat. In a random sample of 400 households 156 say they own a dog or a cat. At 0.10 is there enough evidence to support the society’s claim?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
1. Consider the data showing the number of bikes sold by a specialized market over the past 10
weeks.
Week: 1 2 3 4 5 6 7 8 9 10
Sales: 15 20 17 18 16 22 25 18 20 19
(a). Compute forecasts using a 3-week moving average. Calculate the mean squared error
(MSE).
(b). Use weighted moving average selecting weights for the data values. Calculate the mean
squared error (MSE).
(c). Apply exponential smoothing with the smoothing constant . Calculate the mean
squared error (MSE).
2. The table below shows the price of a house in a specific region in the years 2015 through
2020 (in thousands of $).
Year: 2015 2016 2017 2018 2019 2020
Price: 81 82 83.5 85 87.5 91
Check whether the increasing trend is actual, by removing the inflation effect, using the CPI
(2010 base year):
Year: 2015 2016 2017 2018 2019 2020
CPI: 108 110 113 116 120 125
3. A human society claims that less than 35% of households own a dog or a cat. In a random
sample of 400 households 156 say they own a dog or a cat. At 0.10 is there enough
evidence to support the society’s claim?
4. A production line is designed on the assumption that the time difference between two
operations is 5 minutes. Suppose two independent samples for the two operations yield the
following results:
Operation 1 Operation 2
n1=80 n2=60
Sample mean1=9.5 min Sample mean2=4.7 min
s1=0.7 min s2=0.9 min
At a level of significance 0.05, test the hypothesis that the time difference between two operations is 5 minutes.
5. Based on the results of the following independent samples,
Sample 1 Sample 2
n1=250 n2=200
p1= 0.23 p2=0.18,
consider the hypothesis test:
H0:p1-p2<=0
Ha:p1-p2>o
at a level of significance a) 0.10; b) 0.05.
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