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20. A filling machine in a...

20.

A filling machine in a brewery is designed to fill bottles with 355 ml of hard cider. In practice, however, volumes vary slightly from bottle to bottle. The brewer suspects that the filling machine has been underfilling the bottles. In a sample of 49 bottles, the mean volume of cider is found to be 354 ml, with a standard deviation of 3.5 ml. To determine if the machine is underfilling bottles, the brewer performs a one-sided hypothesis test.

The best formulation of the null hypothesis is:

Source

•

The true mean cider volume of each bottle is 354 ml.

•

The true mean cider volume of each bottle is at least 355 ml.

•

The machine is underfilling the bottles.

•

The machine is underfilling the bottles by 1 ml.

21.

A market research firm wants to find out if men and women feel differently about SilkyTouch facial tissues. In a survey of 90 men, 76% said they had a favorable impression of SilkyTouch. Out of 182 surveyed women, 64% said they had a favorable impression of SilkyTouch.

At a 95% confidence level, which conclusion should the research firm draw?

Source

•

Overall, about 70% of the population has a favorable impression of SilkyTouch.

•

Men and women feel differently about SilkyTouch.

•

More women than men have a favorable impression of SilkyTouch.

•

There is insufficient evidence to show that men and women feel differently about SilkyTouch

22.

A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in Bowie County. Historically, around 62% of the county's registered voters have supported the Uniformians. In a survey of 196 registered voters, 57% indicated that they would vote for the Uniformians in the next election.

Assuming a confidence level of 95% and conducting a one-sided hypothesis test, which of the following should the strategist do?

Source

•

Accept the hypothesis that the proportion of Uniformian voters has not changed.

•

Accept the hypothesis that the proportion of Uniformian voters has decreased.

•

Conclude that the proportion of Uniformian voters is now between 56% and 62%.

•

There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.

23.

A manufacturer of guitar amplifiers markets one of its models, Vagabond, at a power rating of 45 watts. GuitarGod magazine suspects that this rating is inaccurate for this year's model of the amp. In a random sample of 32 units of this year's version of the Vagabond the mean output power is 42 watts, with a standard deviation of 8 watts.

Assuming a confidence level of 95%, which of the following statements do these data support?

Source

•

This year's Vagabond's output power is 45 watts.

•

This year's Vagabond's output power is 42 watts.

•

This year's Vagabond's output power is not 45.

•

None of the above.

24.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable "average monthly temperature" (in degrees Fahrenheit).

At what level of significance is the relationship between ice cream consumption and temperature statistically significant?

Ice Cream Consumption and Temperature

Source

•

0.05

•

0.01

•

0.001

•

All of the above.

25.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable "average monthly temperature" (in degrees Fahrenheit).

Based on this analysis we can conclude:

Ice Cream Consumption and Temperature

Source

•

For every increase of 0.027 degrees in average monthly temperature, average ice cream consumption increases by 1 pint.

•

For every increase of 1 degree in average monthly temperature, average ice cream consumption increases by 0.027 pints.

•

For every increase of 1.797 degrees in average monthly temperature, average ice cream consumption increases by 1 pint.

•

For every increase of 1 degree in average monthly temperature, average ice cream consumption increases by 1.797 pints.

26.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable "average monthly temperature" (in degrees Fahrenheit).

Which of the following statements about the term "1.797" is true?

Ice Cream Consumption and Temperature

Source

•

It tells us the maximum amount above which ice cream consumption cannot possibly grow.

•

It tells us the minimum amount below which ice cream consumption cannot possibly fall.

•

It tells us the x-intercept of the regression equation.

•

It tells us the y-intercept of the regression equation

A filling machine in a brewery is designed to fill bottles with 355 ml of hard cider. In practice, however, volumes vary slightly from bottle to bottle. The brewer suspects that the filling machine has been underfilling the bottles. In a sample of 49 bottles, the mean volume of cider is found to be 354 ml, with a standard deviation of 3.5 ml. To determine if the machine is underfilling bottles, the brewer performs a one-sided hypothesis test.

The best formulation of the null hypothesis is:

Source

•

The true mean cider volume of each bottle is 354 ml.

•

The true mean cider volume of each bottle is at least 355 ml.

•

The machine is underfilling the bottles.

•

The machine is underfilling the bottles by 1 ml.

21.

A market research firm wants to find out if men and women feel differently about SilkyTouch facial tissues. In a survey of 90 men, 76% said they had a favorable impression of SilkyTouch. Out of 182 surveyed women, 64% said they had a favorable impression of SilkyTouch.

At a 95% confidence level, which conclusion should the research firm draw?

Source

•

Overall, about 70% of the population has a favorable impression of SilkyTouch.

•

Men and women feel differently about SilkyTouch.

•

More women than men have a favorable impression of SilkyTouch.

•

There is insufficient evidence to show that men and women feel differently about SilkyTouch

22.

A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in Bowie County. Historically, around 62% of the county's registered voters have supported the Uniformians. In a survey of 196 registered voters, 57% indicated that they would vote for the Uniformians in the next election.

Assuming a confidence level of 95% and conducting a one-sided hypothesis test, which of the following should the strategist do?

Source

•

Accept the hypothesis that the proportion of Uniformian voters has not changed.

•

Accept the hypothesis that the proportion of Uniformian voters has decreased.

•

Conclude that the proportion of Uniformian voters is now between 56% and 62%.

•

There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.

23.

A manufacturer of guitar amplifiers markets one of its models, Vagabond, at a power rating of 45 watts. GuitarGod magazine suspects that this rating is inaccurate for this year's model of the amp. In a random sample of 32 units of this year's version of the Vagabond the mean output power is 42 watts, with a standard deviation of 8 watts.

Assuming a confidence level of 95%, which of the following statements do these data support?

Source

•

This year's Vagabond's output power is 45 watts.

•

This year's Vagabond's output power is 42 watts.

•

This year's Vagabond's output power is not 45.

•

None of the above.

24.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable "average monthly temperature" (in degrees Fahrenheit).

At what level of significance is the relationship between ice cream consumption and temperature statistically significant?

Ice Cream Consumption and Temperature

Source

•

0.05

•

0.01

•

0.001

•

All of the above.

25.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable "average monthly temperature" (in degrees Fahrenheit).

Based on this analysis we can conclude:

Ice Cream Consumption and Temperature

Source

•

For every increase of 0.027 degrees in average monthly temperature, average ice cream consumption increases by 1 pint.

•

For every increase of 1 degree in average monthly temperature, average ice cream consumption increases by 0.027 pints.

•

For every increase of 1.797 degrees in average monthly temperature, average ice cream consumption increases by 1 pint.

•

For every increase of 1 degree in average monthly temperature, average ice cream consumption increases by 1.797 pints.

26.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable "average monthly temperature" (in degrees Fahrenheit).

Which of the following statements about the term "1.797" is true?

Ice Cream Consumption and Temperature

Source

•

It tells us the maximum amount above which ice cream consumption cannot possibly grow.

•

It tells us the minimum amount below which ice cream consumption cannot possibly fall.

•

It tells us the x-intercept of the regression equation.

•

It tells us the y-intercept of the regression equation

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