PSYCH 9A Study Guide - Final Guide: Null Hypothesis, Statistical Hypothesis Testing, Paired Difference Test

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Homework #8
13.4 For each of the following research questions, specify whether the parameter of
interest is one population mean, the population mean of paired differences, or the
difference between the means of two populations.
a. Residents of a neighborhood have been complaining about speeding cars. The
speed limit in the area is 25 miles per hour. The local police monitor the situation
by recording the speed of 100 randomly selected cars. They want to know
whether the mean speed of all cars that drive through the area is higher than 25
miles per hour.
The parameter of interest in this research question will be one population mean because it is
testing the mean speed of cars that drive in the area is 25 miles.
b. Refer to part(a).After collecting the data described in part (a), the police decide to
install an electronic roadside sign that shows cars how fast they are driving. They then
record the driving speed of another 100 randomly selected cars. They want to know
whether the mean speed is lower after installation of the sign than it was beforehand.
The parameter of interest will be the difference between the two populations because it is
comparing how fast the randomly selected cars drive without and with the road sign.
13.8 Refer to Exercises 13.4 and 13.6. Specify the null value that the researchers are
interested in testing, and write the null hypothesis using the appropriate symbol(s) for
the parameter of interest. If you haven’t already done so in Exercise 13.6, make sure
that you specify the population(s) to which the parameter applies.
The parameter of this data will be one population mean because the police is collecting data
about the speeds of 100 randomly selected cars in a speed limit zone. The police will be
testing the mean speeds of cars that drive in this area is 25 miles per hour. The sign of
parameter will be μ.
Null Hypothesis: H0; μ=25
13.10 Explain why the null hypothesis for a significance test is rejected when the p-value
is small rather than when it is large.
A p-value measures how usual a certain outcome will happen in a population, and the null
hypothesis specified the probability of a small outcome would occur in a population. So when
the p-value is small, we can assume that the outcome is not that usual and it might not come
with the distribution specify in the null hypothesis, which we can reject the null hypothesis. If
the p-value is large, it means that the outcome is not unusual in the distribution specify by the
null hypothesis, which will be hard to reject.
13.14 Define the parameter of interest, and then use it to write the null and alternative
hypotheses (in symbols) for each of the following research questions. Make sure you
specify the population to which the parameter applies.
a. Many cars have a recommended tire pressure of 32 psi (pounds per square inch).
At a roadside vehicle safety checkpoint, officials plan to randomly select 50 cars
for which this is the recommended tire pressure and measure the actual tire
pressure in the front left tire. They want to know whether drivers on average
have too little pressure in their tires.
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The parameter of interest in this question will be the population mean tire pressure for the
font left tire of all cars, the sign will be μ. In a sample of n=50, and the recommended tire
pressure of 32 psi, the hypotheses will be:
H0: μ=32
Ha: μ<32
The alternative hypothesis is left-tailed because of the officials’ concern that the left tire will
be underinflated.
b. The box of Yvette’s favorite cereal states that the net contents weigh 12 ounces.
Yvette is suspicious of this claim because the package never seems full to her. She plans
to measure the weight of the contents of the next 20 boxes she buys and find out whether
she is being short-changed.
The parameter of interest for this question will be population mean weight of the cereal
boxes, the sign will be μ.
The hypotheses:
H0: μ=12
Ha: μ<12
The alternative hypothesis is left-tailed is because of her concern that the boxes will be
underweight.
13.22 The dataset cholest on the companion website includes cholesterol levels for heart
attack patients and for a group of control patients. It is recommended that people try to
keep their cholesterol level below 200. The following Minitab output is for the control
patients:
a. What are the null and alternative hypotheses being tested? Write them in symbols.
The null and alternative hypotheses:
H0: μ=200
Ha: μ<200
b. What is the mean cholesterol level for the sample of control patients?
The sample mean is x bar=193.13 (value found in the chart)
c. How many patients were in the sample?
The sample size of the control group n=30
d. Use the formula for the standard error of the mean to show how to compute the value
of 4.07 reported by Minitab.
This is the formula for standard error of the mean.
22.3/squar(30)=4.07
e. What values does Minitab report for the test statistic and the p-value? f. Identify the
numbers that were used to compute the t-statistic, and verify that the reported value is
correct.
The t-test statistic from the Minitab output is -1.69, and p-value is 0.051.
f. Identify the numbers that were used to compute the t-statistic, and verify that the
reported value is correct.
Used the calculator:
μ0=200
x-bar=193.13
Sx=22.3
n=30
μ does not equal to μ0
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Document Summary

The speed limit in the area is 25 miles per hour. The local police monitor the situation by recording the speed of 100 randomly selected cars. They want to know whether the mean speed of all cars that drive through the area is higher than 25 miles per hour. They then record the driving speed of another 100 randomly selected cars. They want to know whether the mean speed is lower after installation of the sign than it was beforehand. The parameter of interest will be the difference between the two populations because it is comparing how fast the randomly selected cars drive without and with the road sign. Specify the null value that the researchers are interested in testing, and write the null hypothesis using the appropriate symbol(s) for the parameter of interest. If you haven"t already done so in exercise 13. 6, make sure that you specify the population(s) to which the parameter applies.

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