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Or a particular consumer product, the mean dollar sales per

retail outlet last

year in a sample of

n

=10 stores was

x

=$3,425 with s = $200. The sales amounts

per outlet are assumed to be normally distributed. Estimate the standard

deviation of dollar sales of this product in all stores las

t year, using a 90 percent

confidence interval.

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Women athletes at the University of Colorado, Boulder, have a long

-term

graduation rate of 67%. Over the past several years, a random sample of 38

women athletes at the school showed that 31 eventually

graduated. Does this

indicate that the population proportion of women athletes who graduate from

the University of Colorado, Boulder, is now more than 67%? Use a 5% level of

significance.

(8pt)

10.

Suppose that it is known from experience that the standard d

eviation of the

weight of 5

-ounce packages of cookies made by a certain bakery is

σ

=0.2 ounce.

To check the whether its production is under control on a given day, that is, to

check whether the true average weight of the package is

5 ounces, employees

select a random sample of 36 packages and find their mean weight is

x

= 5.05

ounces. Since the bakery stands to lose money when

5

μ

>

and customer loses

out when

5

μ

<

, test the null hypothesis

5

μ

=

at the 1 percent level of

significance

using two

-tailed test.

(8pt)

11.

Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic

level of μ

=8.0 parts per billion (ppb) is considered safe for agricultural use. A

well in Texas is sued to water cotton crops. This well is tested on a regular basis

for arsenic. A random sample of 31 tests gave a sample mean of

x

=7.2 ppb

arsenic, with

s

= 1.9 ppb. Does this informatio

n indicate that the mean level of

arsenic in this well is less than 8 ppb? Use

α

= 0.01

(8pt)

12.

Let

x

be a random variable that represents weight loss (in pound) after following

a certain diet for 6 months. After extensive study, it is found that

x

has a no

rmal

distribution with

σ

=5.7 pounds. A new modification of the diet has been

implemented. A random sample of

n

=21 people use the modified diet for 6

months. For these people, the sample standard deviation of weight loss is

s

=3.8

pounds. Does this result indicate that the standard deviation of weight loss for

the modified diet is different (either way) from the standard deviation of weight

loss for the original diet? Use

α

= 0.01

(

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