Stat1342.002
Quiz 7
1. Arsenic occurs naturally in ground water. A mean arsenic level of
μ=8.0 ppb is considered safe for agricultural use. A well in Texas is
used to water cotton crops. This well is tested on a regular basis for
arsenic. A random sample of 37 tests gave a sample mean of 7.2 ppb
of arsenic with standard deviation (s) 1.9 ppb. Does this information
indicate that the mean level of arsenic in this well is less than 8 ppb?
Based on this answer the following
a. Write the null and alternative hypothesis
Null Hypothesis, H0: µ=8
Alternative Hypothesis, H1:µ<8
b. Which of the following tests is applicable:
(i)
Z-test
(ii)
T-Test.
c. The value of the test statistic is t =
7.2  8
1.9 / 37
 -2.5611
d. Which of the following conclusions is?
(a) At α = 0.05, we do not reject H0.
(b) At α = 0.05, we reject H0.
(c) At α = 0.05, we accept H0.
(d) Both a and c.
2.
Suppose you conducted a hypothesis test and you didn't reject the
null hypothesis at 10% level of significance. If another student wants to use
5% level of significance, then which of the following is true? Also, mention
your reason.
(a) At α = 0.05, we do not reject H0.
(b) At α = 0.05, we reject H0.
(c) Can't conclude anything based on the given information.
Reason: “You didn't reject the null hypothesis at 10% level of significance”,
i.e. p-value>0.1(>0.05). Hence, at α = 0.05, we do not reject H0.
3.
A lodge advertises that 75% of its guests catch northern pike over 20
pounds. Suppose that last summer 64 out of a random sample of 83 guests
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did, catch northern pike weighing over 20 pounds. Does this indicate that
the percentage of guests who catch pike over 20 pounds is different from
75%?
a. Write the null and alternative hypothesis
Null Hypothesis, H0: p=0.75
Alternative Hypothesis, H1: p≠0.75
64
 0.77
83
0.77  0.75
 0.42
b. The value of the test statistic is Z 
0.75  0.25
83
pˆ 
c. The p-value is: 0.6744
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