Question

hypothesis that
are
Given a the data below, test the
that
the mean of 3 population
equal let
d= 0.05
Sample Sample II Sample
30
70
45
55
65
38
62
60
45
50
42
66​

Answer 1

Answer:

Step 1: Determine the hypotheses.

We did this on the previous page. The hypotheses are:

H0: p = 0.80

Ha: p > 0.80

where p is the proportion of college students ages 18 to 23 who have health insurance now.

Step 2: Collect the data.

In this random sample of 800 college students, 83% have health insurance. If 80% of all college students have health insurance, is this 3% difference statistically significant or due to chance? We need to find a P-value to answer this question. We must determine if we can use this data in a hypothesis test.

First note that the data are from a random sample. That is essential. Now we need to determine if a normal model is a good fit for the sampling distribution. Since we assume that the null hypothesis is true, we build the sampling distribution with the assumption that 0.80 is the population proportion. We check the following conditions, using 0.80 for p:

\displaystyle np=(800)(0.80)=640\text{ }\mathrm{and}\text{ }n(1-p)=(800)(1-0.80)=160np=(800)(0.80)=640 and n(1−p)=(800)(1−0.80)=160

Because these are both more than 10, we can use the normal model to find the P-value.

Step 3: Assess the evidence.

Now that we know that the normal distribution is an appropriate model for the sampling distribution, our next goal is to determine the P-value. The first step is to determine the z-score for the observed sample proportion (the data).

The sample proportion is 0.83. Recall from Linking Probability to Statistical Inference that the formula for the z-score of a sample proportion is as follows:

Z

=

ˆ

p

−

p

√

p

(

1

−

p

)

n

For this example, we calculate:

\displaystyle Z=\frac{0.83-0.80}{\sqrt{\frac{0.80(1-0.80)}{800}}}\approx 2.12Z=

√

800

0.80(1−0.80)

0.83−0.80

≈2.12

Explanation:

Hope you find this helpful.......