J
Jon D
Guest
value of test statistic, w? For each problem show: null and alternate hypothesis, formula for test
statistic, value of test statistic, when to reject, decision on null
hypothesis, and answer to the question asked by the problem. .
If a value of alpha is not given, select an appropriate value of alpha.
1. A theatre owner wishes to know if the percentage of people buying
popcorn is the same for matinees as it is for evening shows. In
sampling, 18 of 75 people attending matinees and 72 of 225 people
at evening shows bought popcorn. Using .05 level of significance,
do the samples indicate that there is a difference?
2. A random sample of 200 people attending movies had an average age of
18.7 years with standard deviation 7.6 years. At the .05 level of
significance, can we say the average age is not 20?
3. A sample of 12 movies in 2001 averaged 96 minutes with standard
deviation 13 minutes and a sample of 10 movies from 1991 averaged 109
minutes with standard deviation 15 minutes. Can we say that movies
are shorter than they were 10 years ago at level of significance 5%?
4. A newspaper says that two-thirds of the classified ads it runs for
selling items result in sales within one week. If a sample of 400 ads
had 63% result in sales within one week, is there enough evidence to
say their claim is wrong at the .01 level of significance?
5. 5 people had their blood pressure measured before and after eating a
meal; the measurements are below. Is there enough evidence to say
that eating a meal increases blood pressure (at .05 level of
significance)?
before meal 125 143 138 129 120
after meal 132 147 137 138 126
6. It is claimed that the average car on the road is more than 7.5 years
old. If a random sample of 50 cars had an average age of 8.6 years
with standard deviation 3.6 years:
a) set up the null and alternate hypotheses to see if the claim is true.
b) calculate the test statistic
c) calculate the significance of the test statistic (p-value)
d) state your decisions for the following levels of significance:
.06, .03, .015, .0075
7. A new hybrid seed claims an average yield of 76; a sample of 20
values had an average yield of 70 with variance 343. Using
significance level .05, can we say that the actual yield is less than
the claimed value?
8. Before an advertising campaign pushing mass transit, a sample of 45
buses had an average of 17.2 riders with standard deviation 5.7 riders.
After the campaign, a sample of 60 buses averaged 21.8 riders with
standard deviation 8.3 riders. Is there enough evidence to say that
the average number of riders has increased?
9. A sample of 7 days averaged 175 sales per day with variance 817. At
the .10 level of significance, is it reasonable to say that the
average number of sales per day is 200?
statistic, value of test statistic, when to reject, decision on null
hypothesis, and answer to the question asked by the problem. .
If a value of alpha is not given, select an appropriate value of alpha.
1. A theatre owner wishes to know if the percentage of people buying
popcorn is the same for matinees as it is for evening shows. In
sampling, 18 of 75 people attending matinees and 72 of 225 people
at evening shows bought popcorn. Using .05 level of significance,
do the samples indicate that there is a difference?
2. A random sample of 200 people attending movies had an average age of
18.7 years with standard deviation 7.6 years. At the .05 level of
significance, can we say the average age is not 20?
3. A sample of 12 movies in 2001 averaged 96 minutes with standard
deviation 13 minutes and a sample of 10 movies from 1991 averaged 109
minutes with standard deviation 15 minutes. Can we say that movies
are shorter than they were 10 years ago at level of significance 5%?
4. A newspaper says that two-thirds of the classified ads it runs for
selling items result in sales within one week. If a sample of 400 ads
had 63% result in sales within one week, is there enough evidence to
say their claim is wrong at the .01 level of significance?
5. 5 people had their blood pressure measured before and after eating a
meal; the measurements are below. Is there enough evidence to say
that eating a meal increases blood pressure (at .05 level of
significance)?
before meal 125 143 138 129 120
after meal 132 147 137 138 126
6. It is claimed that the average car on the road is more than 7.5 years
old. If a random sample of 50 cars had an average age of 8.6 years
with standard deviation 3.6 years:
a) set up the null and alternate hypotheses to see if the claim is true.
b) calculate the test statistic
c) calculate the significance of the test statistic (p-value)
d) state your decisions for the following levels of significance:
.06, .03, .015, .0075
7. A new hybrid seed claims an average yield of 76; a sample of 20
values had an average yield of 70 with variance 343. Using
significance level .05, can we say that the actual yield is less than
the claimed value?
8. Before an advertising campaign pushing mass transit, a sample of 45
buses had an average of 17.2 riders with standard deviation 5.7 riders.
After the campaign, a sample of 60 buses averaged 21.8 riders with
standard deviation 8.3 riders. Is there enough evidence to say that
the average number of riders has increased?
9. A sample of 7 days averaged 175 sales per day with variance 817. At
the .10 level of significance, is it reasonable to say that the
average number of sales per day is 200?