Ch 10 ICP #3

1) The level of dissolved oxygen (DO) in a stream or river is an important indicator of the water’s ability to support aquatic life. A researcher measures the DO level at 15 randomly chosen locations along a stream. A DO level below 5 mg/l puts aquatic life at risk. Perform a hypothesis test to determine if we have significant evidence to conclude the aquatic life in this stream is at risk? Here are the results in mg per liter.

4.53 5.04 3.29 5.23 4.13 5.5 4.83 4.4

5.42 6.38 4.01 4.66 2.87 5.73 5.55

Assume sigma = 3.637

Ch 10 ICP #32) At the Hawaiian Pineapple Company managers are interested in the size of the pineapples grown in the fields. Last year, the mean weight of the pineapples harvested from one field was 31 oz. A new irrigation system was installed in the field after the growing season. Managers wonder whether this change will affect the mean weight of future pineapples grown in the field. They take an SRS of 50 pineapples and find the mean to be 31.935 oz. Sigma is known to be 2.4 oz. Perform a significance test to determine if the weight of the pineapples has changed.

Ch 10 ICP #3

3) How well materials conduct heat matters when designing houses for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface. In these units, glass has a conductivity about 1. The national institute of Standards and Technology provides exact data on properties of materials. Here are the measurements of heat conductivity of 11 randomly selected pieces of a particular type of glass.

1.11 1.07 1.11 1.07 1.12 1.08 1.08 1.18 1.181.18 1.12

Is there convincing evidence that the conductivity of this type of glass is greater than 1?Assume sigma = 0.05.

Ch 10 ICP #3

4) The one sample z statistic from a sample of n = observations for the 2 sided test of

Has the z-score z = -1.12

a) Find the p-value for this testb) Is it signifcant at the 1% level? What about the 5% level?c) Redo parts a and b using an alternative hypothesis of

: 64

: 64o

a

H

H

: 64aH

Ch 10 ICP #3

5) Bottle of a popular soda are supposed to contain 300 ml of soda. There is some variation from bottle to bottle because the machinery filling the bottles is not perfect. From experience the distribution of amounts is approximately normal. An inspector measures the contents of 6 randomly selected bottles from a single day’s production. The results are:

299.4 297.7 301 298.9 300.2 297

Do these data provide convincing evidence at the 1% level that the mean amount of cola in all the bottles filled that day differs from the target value of 300 ml?