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Write an inequality to represent the phrase: The sum of a number an 6 is no less than 31

Leviafan [203]

The inequality that represents this phrase is n+6 > 31.

5 0

3 years ago

A magazine provided results from a poll of 500500 adults who were asked to identify their favorite pie. Among the 500500 respon

Komok [63]

Answer:

99% confidence interval is wider as compared to the 80% confidence interval.

Step-by-step explanation:

We are given that a magazine provided results from a poll of 500 adults who were asked to identify their favorite pie.

Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as plus or minus ±3 percentage points.

The pivotal quantity for the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who chose chocolate pie = 14%

n = sample of adults = 500

p = true proportion

Now, the 99% confidence interval for p = $\hat p \pm Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

Here, $\alpha$ = 1% so $(\frac{\alpha}{2})$ = 0.5%. So, the critical value of z at 0.5% significance level is 2.5758.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.03 for 99% interval.

So, 99% confidence interval for p = $0.14 \pm2.5758 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

= [0.14 - 0.03 , 0.14 + 0.03]

= [0.11 , 0.17]

Similarly, 80% confidence interval for p = $0.14 \pm 1.2816 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

Here, $\alpha$ = 20% so $(\frac{\alpha}{2})$ = 10%. So, the critical value of z at 10% significance level is 1.2816.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.02 for 80% interval.

So, 80% confidence interval for p = [0.14 - 0.02 , 0.14 + 0.02]

= [0.12 , 0.16]

Now, as we can clearly see that 99% confidence interval is wider as compared to 80% confidence interval. This is because more the confidence level wider is the confidence interval and we are more confident about true population parameter.

5 0

4 years ago

From the set {80, 19, 11}, use substitution to determine which value of x makes the equation true. 8x = 88 A. none of these B. 1

mel-nik [20]

Answer:

C. 11

Step-by-step explanation:

Substituting, we have ...

8{80, 19, 11} ?= 88

{640, 152, 88} ?= 88

The value from the set that makes the equation true is x = 11.

_____

Alternate methods of solution (other than substitution)

It can be easier to make use of your knowledge of factoring:

8x = 8·11

x = 11

Or to make use of your knowledge of numbers (place value):

8·10 = 80

so x will not be very different from 10.

3 0

3 years ago

If y varies directly as x, and x = 48 when y = 6, find y when x = 12.

pentagon [3]

Answer: Each time the pentagon is rotated , it maps back onto itself. There are five values of for which the pentagon maps back onto itself. This is the same as the number of sides of the pentagon.

6 0

3 years ago

Read 2 more answers

A researcher claims that the average annual salary of part-time community college instructors is at least $45,000. To test this

Doss [256]

Answer:

See explanation

Step-by-step explanation:

Solution:-

- The researcher claims :

" the average annual salary of part-time community college instructors is at least $45,000 "

- We will extract the claim made by the researcher to be the Null hypothesis:

Null Hypothesis : μ ≥ $45,000

- Any statement otherwise, or point of rejection criteria will denote the Alternate hypothesis that disbands the claim that:

" the average annual salary of part-time community college instructors is less than $45,000 " :

Alternate Hypothesis : μ < $45,000

- This type of test with a sample size of n = 25 < 30 and population standard deviation is also not given hints the use t-test statistics and t-critical value reject the claim.

Lower tail - one sample - T-test.

6 0

3 years ago