Q Se ction to Hypothesis Testing 13. Researchers at a National Weather Center in the northeastern United States recorded the number of 90° days each year since records first started in 1875. The numbers form a normal shaped distribution with a mean of u = 9.6 and a standard deviation of o = 1.9. To see if the data showed any evidence of global warming, they also computed the mean number of 90° days for the most recent n = 4 years and obtained M = 11.85. Do the data indicate that the past four years have had significantly more 90° days than would %3D be expected for a random sample from this population? Use a one-tailed test with a = .05. %3D Answer + 14. Montarello and Martens (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of = 100 and a standard deviation of o = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 104, is this result sufficient to conclude that inserting the easy questions improves student %3D performance? Use a one-tailed test with a = .01. 15. Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries can reduce and even reverse these age-related declines, at least in laboratory rats (Joseph et al., 1999). Based on these results, one might theorize that the same antioxidants might also benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, %3D articinont o deilku doge of a blusher Sunplenment that is very hiơh in antioxidants. After

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Question 14

Q Se
ction to Hypothesis Testing
13. Researchers at a National Weather Center in the northeastern United States recorded the number of 90°
days each year since records first started in 1875. The numbers form a normal shaped distribution with a
mean of u = 9.6 and a standard deviation of o = 1.9. To see if the data showed any evidence of global
warming, they also computed the mean number of 90° days for the most recent n = 4 years and obtained
M = 11.85. Do the data indicate that the past four years have had significantly more 90° days than would
%3D
be expected for a random sample from this population? Use a one-tailed test with a = .05.
%3D
Answer +
14. Montarello and Martens (2005) found that fifth-grade students completed more mathematics problems
correctly when simple problems were mixed in with their regular math assignments. To further explore
this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that
produces a normal distribution of scores with a mean of = 100 and a standard deviation of o = 18. The
researcher modifies the test by inserting a set of very easy problems among the standardized questions,
and gives the modified test to a sample of n = 36 students. If the average test score for the sample is
M = 104, is this result sufficient to conclude that inserting the easy questions improves student
%3D
performance? Use a one-tailed test with a = .01.
15. Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the
results from other research suggest that the antioxidants in foods such as blueberries can reduce and even
reverse these age-related declines, at least in laboratory rats (Joseph et al., 1999). Based on these results,
one might theorize that the same antioxidants might also benefit elderly humans. Suppose a researcher is
interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65,
%3D
articinont o deilku doge of a blusher Sunplenment that is very hiơh in antioxidants. After
Transcribed Image Text:Q Se ction to Hypothesis Testing 13. Researchers at a National Weather Center in the northeastern United States recorded the number of 90° days each year since records first started in 1875. The numbers form a normal shaped distribution with a mean of u = 9.6 and a standard deviation of o = 1.9. To see if the data showed any evidence of global warming, they also computed the mean number of 90° days for the most recent n = 4 years and obtained M = 11.85. Do the data indicate that the past four years have had significantly more 90° days than would %3D be expected for a random sample from this population? Use a one-tailed test with a = .05. %3D Answer + 14. Montarello and Martens (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of = 100 and a standard deviation of o = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 104, is this result sufficient to conclude that inserting the easy questions improves student %3D performance? Use a one-tailed test with a = .01. 15. Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries can reduce and even reverse these age-related declines, at least in laboratory rats (Joseph et al., 1999). Based on these results, one might theorize that the same antioxidants might also benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, %3D articinont o deilku doge of a blusher Sunplenment that is very hiơh in antioxidants. After
Expert Solution
Step 1

From the provided information,

Sample size (n) = 36

Population Mean (µ) = 100

Population standard deviation (σ) = 18

Sample mean (M) = 104

Level of significance (α) = 0.01

The hypotheses can be constructed as:

Null hypothesis H0: µ = 100

Alternative hypothesis H1: µ >100

The test is right tailed. The population standard deviation is given so the z distribution will be used.

 

Step 2

The value of the test statistic can be obtained as:

Statistics homework question answer, step 2, image 1

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