For each store, what is the ratio of the number of cans to the price?

In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a samp

dsp73

Answer:

$(0.411-0.7) - 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.4401$

$(0.411-0.7) + 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.1380$

We are confident at 95% that the difference between the two proportions is between $-0.4401 \leq p_B -p_A \leq -0.1380$

1. -.4401 ≤ p1 - p2 ≤ -.1380

4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

Step-by-step explanation:

In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a sample of 80 mail carriers, 56 had received animal bites. Is there a significant difference in the proportions? Use a 0.05. Find the 95% confidence interval for the difference of the two proportions. Sellect all correct statements below based on the data given in this problem.

1. -.4401 ≤ p1 - p2 ≤ -.1380

2. -.4401 ≤ p1 - p2 ≤ .1380

3. The rate of mail carriers being bitten in San Jose is statistically greater than the rate San Francisco at α = 5%

4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

5. The rate of mail carriers being bitten in San Jose and San Francisco are statistically equal at α = 5%

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_1$ represent the real population proportion for San Jose

$\hat p_1 =\frac{30}{73}=0.411$ represent the estimated proportion for San Jos

$n_1=73$ is the sample size required for San Jose

$p_2$ represent the real population proportion for San Francisco

$\hat p_2 =\frac{56}{80}=0.7$ represent the estimated proportion for San Francisco

$n_2=80$ is the sample size required for San Francisco

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_1 -\hat p_1) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.411-0.7) - 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.4401$

$(0.411-0.7) + 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.1380$

We are confident at 95% that the difference between the two proportions is between $-0.4401 \leq p_B -p_A \leq -0.1380$

Since the confidence interval contains all negative values we can conclude that the proportion for San Jose is significantly lower than the proportion for San Francisco at 5% level.

Based on this the correct options are:

1. -.4401 ≤ p1 - p2 ≤ -.1380

4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

8 0

3 years ago

Simplify (−3c3w5)3 ..................................

ivanzaharov [21]

Answer:

= −9 c 3w 5

≡≡≡≡≡≡≡≡≡≡≡≡≡

5 0

4 years ago

10 2/6 - 7 5/6 i know its prob easy but i need help

miv72 [106K]

Answer: 2 1/3

Explanation:

10 2/6 - 7 5/6

You can make both a fraction by multiplying the denominator by the whole number, and then adding the numerator to that number, and keeping the denominator the same. So, 10*6 = 60 and 60 + 2 = 62 and you keep the denominator as 6, which would make 62/6

7*6 = 42 and 42 + 5 = 47 so 7 5/6 becomes 47/6

10 2/6 is equivalent to 62/6

7 5/6 is equivalent to 47/6

This just makes it easier to look at.

Now you just work through the equation.

62/6 - 47/6 = 15/6

15/6 = 2 3/6 = 2 1/3

3 0

3 years ago

Seven times a number n and 4

WARRIOR [948]

anything above 28

Step-by-step explanation:

Seven times 4 is 28, times any number is anything 28 and above

5 0

3 years ago

Read 2 more answers

Help plz I’m not good at this

Natalka [10]

Answer:

The correct answer is A. 1/8

Step-by-step explanation:

Let's solve (1/3 * 9/16) / 1 1/2 = x

(1/3 * 9/16) / 1 1/2 = x

9/48 / 1 1/2 = 9/48 * 2/3 = 18/144

18/144, we can simplify dividing by 18 at the numerator and the denominator, this way:

x = 18 ÷ 18/ 144 * 18 = 1/8

The correct answer is A. 1/8

4 0

3 years ago