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 =
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 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
b. The value of the test statistic is
c. The p-value is: 0.6744
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