Stats Assignment 5 on Hypothesis Tests

1/ The yield of alfalfa from 6 test plots is 1.4, 1.8, 1.1, 1.9, 2.2, and 1.2 tons per acre.
Test at the 5% level of significance whether this supports the claim that
the average yield for this kind of alfalfa is 1.5 tons per acre.

(5)

2/ In the comparison of 2 kinds of paint, a consumer-testing service found that
4 one-gallon cans of brand A covered an average of 514 sq. ft. with a standard deviation
of 32 sq. ft., while 4 one-gallon cans of brand B paint covered an average of 487 sq. ft.
with a standard deviation of 27 sq. ft.
Use the 5% level of significance to test whether the difference between the
two sample means is significant.

(5)

3/ The following data were obtained in an experiment designed to check whether
there is a difference in the weights (grams) obtained with two different scales:

 SPECIMEN SCALE 1 SCALE 2 1 12.13 12.17 2 17.56 17.61 3 9.33 9.35 4 11.4 11.42 5 28.62 28.61 6 10.25 10.27 7 23.37 23.42 8 16.27 16.26 9 12.4 12.45 10 24.78 24.75

Use the 1% level of significance to test whether the difference between
the means of the weights obtained with the two scales is significant.

(5)

4/ Samples of 50 freshmen from two Universities were given a special test
to determine their knowledge of history. The average score from University A
was 67.4 with a standard deviation of 5. The average score from university B was 62.8
with a standard deviation of 4.6.
Test at the 5% level of significance whether the difference between
the two samples is significant.

(5)

5/ To test the effectiveness of a new drug, 80 patients at a clinic were given the drug
and 80 others were given a placebo. If 56 of the patients who received the drug
and 38 of those who received the placebo felt a beneficial effect, what can we
conclude at the 1% level of significance about the effectiveness of the new drug?

(5)

6/ The student newspaper interviewed a random sample of 200 male students and
found that 150 were in favor of having a homecoming dance.
A random sample of 400 females revealed that 312 were in favor of the dance.
At the 10% significance level, does the sample evidence show that there is a
difference between the proportion of males and females favoring a dance?

(5)

7/ A traffic engineer is studying the traffic pattern on a four-lane inbound expressway.
For an hour, he counts the number of vehicles using each of the four lanes.
The results are as follows:

 LANE VEHICLES 1 100 2 80 3 60 4 60

At the 5% significance level, test the hypothesis that traffic uses all four lanes equally.

(5)

8/ Studies have shown that in the past, 25.2% of the used cars bought in a particular
city are subcompacts, 52.9% are mid-sized and 21.9% are full-sized cars.
A sample of 500 sales during the first quarter revealed that 129 were subcompacts,
258 were mid-sized and 113 were full-sized cars.
Test at the 5% level of significance that there has been no change in the buying
habits with respect to used cars in that city.

(5)

9/ The table shows the results of a study in which independent random samples of
workers in 3 parts of the country were asked whether they feel that unemployment
or inflation is a more serious problem:

 northeast midwest southwest total unemployment 87 73 66 226 inflation 113 77 84 274 total 200 150 150 500

Test at the 5% level of significance whether the differences among the sample proportions
of workers who chose unemployment are significant.

(5)

TOTAL (45)

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