Question

A hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50%. A random sample of 152 customers that purchased seltzer is acquired (assume no customer purchases more than one six pack at a time, alcoholic or not); the sample proportion of these purchases that are alcoholic is obtained. From this sample, a test statistic of 2.60 is calculated, which has a corresponding P-value of 0.0047. Which of the following is true? a. None of these statements is true. b. The probability that, in a random sample of 152 customers purchasing seltzers, more than 50% of those customers will have purchased alcoholic seltzer is 0.0047. c. The probability the null hypothesis is true is 0.0047. d. The probability that 50% of customers purchasing seltzers will be purchasing alcoholic seltzer on any given day is 0.0047. e. The probability the null hypothesis is true is 1-0.0047 = 0.9953. Which of the following are true of P-values? a. Their calculation in a hypothesis test depends on the alternative hypothesis HA. b. They are between 0 and 1. c. They are calculated assuming the null hypothesis H0 is true in a hypothesis test. d. Together with the significance level α, they determine whether or not we reject the H0. e. They represent the probability the null hypothesis H0 is true in a hypothesis test. f. They are used to determine the margin of error of confidence intervals. A fish biologist hypothesizes that the proportion of fish in Lake Ontario that are Black Carp has increased. A study conducted several years ago found that 15% of fish in Lake Ontario were Black Carp. Of 300 randomly sampled fish from Lake Ontario, the biologist finds that 96 are Black Carp. Select from the following the test that best reflects the biologist’s hypothesis. a. H0: p = 0.15 vs. Ha: p ≠ 0.15 b. H0: p = 0.15 vs. Ha: p > 0.15 c. H0: p = 0.15 vs. Ha: p = 0.32 d. H0: p = 0.32 vs. Ha: p > 0.32 e. H0: p = 0.15 vs. Ha: p < 0.15 Suppose that the biologist tests the following hypothesis: H0: p = 0.25 vs. HA: p > 0.25 Where p is the true population proportion of Black Carp in Lake Huron. Of 200 randomly sampled fish from Lake Huron, the biologist finds that 18% are Black Carp. Select from the following options the correct z-score and P-value associated with this hypothesis test. a. z = -2.58; P-value = 0.0049 b. z = -2.29; P-value = 0.0110 c. The hypothesis test cannot be performed because requisite assumptions have not been satisfied. d. z = -2.58; P-value = 0.9951 e. z = -2.29; P-value = 0.9890

A hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50%. A random sample of 152 customers that purchased seltzer is acquired (assume no customer purchases more than one six pack at a time, alcoholic or not); the sample proportion of these purchases that are alcoholic is obtained. From this sample, a test statistic of 2.60 is calculated, which has a corresponding P-value of 0.0047.

Which of the following is true?
a. None of these statements is true.
b. The probability that, in a random sample of 152 customers purchasing seltzers, more than 50% of those customers will have purchased alcoholic seltzer is 0.0047.
c. The probability the null hypothesis is true is 0.0047.
d. The probability that 50% of customers purchasing seltzers will be purchasing alcoholic seltzer on any given day is 0.0047.
e. The probability the null hypothesis is true is 1-0.0047 = 0.9953.

Which of the following are true of P-values?
a. Their calculation in a hypothesis test depends on the alternative hypothesis HA.
b. They are between 0 and 1.
c. They are calculated assuming the null hypothesis H0 is true in a hypothesis test.
d. Together with the significance level α, they determine whether or not we reject the H0.
e. They represent the probability the null hypothesis H0 is true in a hypothesis test.
f. They are used to determine the margin of error of confidence intervals.

A fish biologist hypothesizes that the proportion of fish in Lake Ontario that are Black Carp has increased. A study conducted several years ago found that 15% of fish in Lake Ontario were Black Carp. Of 300 randomly sampled fish from Lake Ontario, the biologist finds that 96 are Black Carp. Select from the following the test that best reflects the biologist’s hypothesis.
a. H0: p = 0.15 vs. Ha: p ≠ 0.15
b. H0: p = 0.15 vs. Ha: p > 0.15
c. H0: p = 0.15 vs. Ha: p = 0.32
d. H0: p = 0.32 vs. Ha: p > 0.32
e. H0: p = 0.15 vs. Ha: p < 0.15

Suppose that the biologist tests the following hypothesis:
H0: p = 0.25 vs. HA: p > 0.25
Where p is the true population proportion of Black Carp in Lake Huron. Of 200 randomly sampled fish from Lake Huron, the biologist finds that 18% are Black Carp. Select from the following options the correct z-score and P-value associated with this hypothesis test.
a. z = -2.58; P-value = 0.0049
b. z = -2.29; P-value = 0.0110
c. The hypothesis test cannot be performed because requisite assumptions have not been satisfied.
d. z = -2.58; P-value = 0.9951
e. z = -2.29; P-value = 0.9890

Added by Juana L.

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