What is the approximate area of the shaded sector in the circle shown below?

The students at Norton School were asked to name their favorite type of pet. Of the 430ilar results, about students surveyed, 25

elena-s [515]

Answer: 60

Step-by-step explanation:

From the question, we are informed that 430 students were surveyed and 258 said that their favorite type of pet was a dog. The fraction/decimal of those that chose dog as their favorite pet will be:

= 258/430

= 3/5

= 0.6

Suppose that only 100 students were surveyed, the number of students that would say that a dog is their favorite types of pet will be:

= 0.6 × 100

= 60

5 0

3 years ago

Suppose that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage

Zigmanuir [339]

Answer:

We conclude that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%.

Let p = population percentage of blue candies

So, Null Hypothesis, $H_0$ : p = 29% {means that the percentage of blue candies is equal to 29%}

Alternate Hypothesis, $H_A$ : p $\neq$ 29% {means that the percentage of blue candies is different from 29%}

The test statistics that will be used here is One-sample z-test for proportions;

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

where, $\hat p$ = sample proportion of blue coloured candies = 28%

n = sample of colored candies = 100

So, the test statistics = $\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }$

= -0.22

The value of the z-test statistics is -0.22.

Also, the P-value of the test statistics is given by;

P-value = P(Z < -0.22) = 1 - P(Z $\leq$ 0.22)

= 1 - 0.5871 = 0.4129

Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29%.

4 0

3 years ago

Explain how you could estimate 22% of 78 to check if your answer is reasonable.

Sedbober [7]

Answer:

Step-by-step explanation:

you could think that 22% is close to 25% , so one forth of it, 1/4

78 percent is close to 80

1/4 of 80 is 20

actually 78*22/100=17.16

7 0