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In a sample of 150 men, 135 said that they had less leisure time today than they had 10 years ago. In a random sample of 250 women, 239 women said that they had less leisure time than they had 10 years ago. At α  = 0.10, is there a difference in the proportions?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

(1 point) 1. In a study of red/green color blindness, 850 men and 2450 women are randomly selected and tested. Among the men, 72 have red/green color blindness. Among the women, 5 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.

The test statistic is

The p-value is

 Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.01% significance level?

A. Yes

B. No

2. Construct the 99% confidence interval for the difference between the color blindness rates of men and women.

Which of the following is the correct interpretation for your answer in part 2?

A. We can be 99% confident that the difference between the rates of red/green color blindness men and women lies in the interval

B. There is a 99% chance that the difference between the rates of red/green color blindness men and women lies in the interval

C. We can be 99% confident that the difference between the rates of red/green color blindness men and women in the sample lies in the interval

D. None of the above.

 

A random sample of 337 college students was asked whether or not they were registered to vote. We wonder if there is an association between a student's sex and whether the student is registered to vote. The data are provided in the tables below (expected counts are in parantheses) (All the conditions are satisfied-don't worry about checking them).

Write appropriate hypotheses:

(a) Mean of the registered Men equals the mean of the registered registered women.

Mean of the registered Men differs from the mean of the registered women.

(b) student's sex is independent of whether the student is registered to vote.

  student's sex is not independent of whether the student is registered to vote.

(c) There is no linear correlation between sex and whether a student is registered to vote

There is linear correlation between sex and whether a student is registered to vote

(d) Let d= Registerd-Note Registered

The mean difference in registered is zero.

The mean difference in registered is less than zero.

(e)  

 

 

Never forget that even small effects can be statistically significant if the samples are large. During a three-year period, 8 of the 57 headed by men and 6 of the 35 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the p-value for the hypothesis that the same proportion of women's and men's businesses fail. (Use two-sided alternative). What can we conclude (use alpha as 0.05)?

The p-value was ___________ so we conclude that ____________.

 

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is 180 out of 1050 businesses headed by women and 240 out of 1710 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude?

The p-value was ___________ so we conclude that ____________.

c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a p-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses that fail for the settings of both (a) and (b).

Interval for smaller samples: ___________ to ___________.

Interval for larger samples: ___________ to ___________.

What is the effect of larger samples on the confidence interval?

 

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