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13. Let P(x) be the predicate,"4x + 1 is even." (a) Is P(5) true or false? (b) What, if anything, can you conclude about 3xP(x) from the truth value of P(5)? (c) What, if anything, can you conclude about VxP(x) from the truth value of P(5)?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

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?

 

Determine whether the statement is true or false. To estimate the value of p, the population proportion of successes, use the point estimate x. 

A. False, to estimate the value of p, use the point estimate  

B. False, to estimate the value of p, use the point estimate  

C. True, to estimate the value of p, use the point estimate  

D. False to estimate the value of p, use the point estimate  

 

Given the following hypothesis: A random sample of six resulted in the following values: 118, 105, 112, 119, 105, and 111. Assume a normal population. Using the .05 significance level, can we conclude the mean is different from 100? a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis? d.Estimate the p-value

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