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Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. The following table displays the data on yield (lb/acre).

(a) How can the Random condition be satisfied in this study?

(b) Perform an appropriate test to help answer the research question. Assume that the Random condition is met. What conclusion would you draw?

Short Answer

Expert verified

a). In each pair of adjacent plots, you randomly allocate one of the plots to be planted with regular barley seeds, while the adjacent plot will then be planted with kiln-dried seeds.

b). There is not sufficient evidence to support the claim.

Step by step solution

01

Part (a) Step 1: Given Information

02

Part (a) Step 2: Explanation

Random sampling provides us with non-aligned data from the population. When samples are collected in an erroneous manner, the data is prone to intolerance.

You will randomly assign one plot to be planted with conventional barley seeds, while the next plot will be planted with kiln-dried seeds in each pair of adjacent plots.

03

Part (b) Step 1: Given Information

04

Part (b) Step 2: Explanation

Determine the difference between "Kiln" and "Regular" for each pair.

05

Part (b) Step 3: Explanation

The mean is the sum of all values divided by the number of values:

x=106-20++127+2411

33.7273

nis the number of values in the data set.

The variance is the sum of squared deviations from the mean divided by n-1:

localid="1650366695337" s2=(106-33.7273)2+.+(24-33.7273)211-1

3980.5620

The standard deviation is the square root of the variance:

localid="1650366712856" s=3980.5620

66.1711

06

Part (b) Step 4: Explanation

Determine the hypotheses:

H0:=0

Ha:>0

Determine the value of the test statistic:

localid="1650366606373" t=x-0s/n

=33.7273-066.1711/11

=1.690

The P-value is the chance of getting the test statistic's result, or a number that is more severe. The P-value is the number (or interval) in Table B's column title that corresponds to the t-value in row localid="1650366573990" n-1=11-1

=10:

0.05<P<0.10

The null hypothesis is rejected if the P-value is less than the significance level.

P>0.05=5%Fail to rejectH0

There is not sufficient evidence to support the claim.

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Most popular questions from this chapter

Study more! The significance test in Exercise 76yields a P-value of 0.0622.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 76? Why?

(b) Which of the following changes would give the test a higher power to detect =120minutes: using =0.01or =0.10? Explain.

鈥淚 can鈥檛 get through my day without coffee鈥 is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). (a) One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday鈥檚 test and one cup of coffee before Wednesday鈥檚 test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

(b) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory.

A change is made that should improve student satisfaction with the parking situation at your school. Right now, 37% of students approve of the parking that鈥檚 provided. The null hypothesis H0:p^=0.37is tested against the alternativeHd:p^0.37.

You are thinking of conducting a one-sample t-test about a population mean M using a 0.05 significance level. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct?

(a) You should not carry out the test because the population does not have a Normal distribution.

(b) You can safely carry out the test if your sample size is large and there are no outliers.

(c) You can safely carry out the test if there are no outliers, regardless of the sample size.

(d) You can carry out the test only if the population standard deviation is known.

(e) The t procedures are robust鈥攜ou can u

As part of its 2010 census marketing campaign, the U.S. Census Bureau advertised

鈥10 questions, 10 minutes鈥攖hat鈥檚 all it takes.鈥 On the census form itself, we read, 鈥淭he

U.S. Census Bureau estimates that, for the average household, this form will take

about 10 minutes to complete, including the time for reviewing the instructions and

answers.鈥 We suspect that the actual time it takes to complete the form may be longer

than advertised.

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