1)A sample of 17 patients in a hospital had these hemoglobin readings (grams): 112 120 98 55 71 35 99 124 64
150 150 55 100 132 20 70 93
Find a 95% confidence interval for the hemoglobin reading for all the patients in the hospital.

2)A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval for the true proportion of men who applied to the nursing program.

3)Average undergraduate cost for tuition, fees, room, and board for all institutions last year was $19,410. A random sample of costs this year for 40 institutions of higher learning indicated that the sample mean was $22,098, and the sample standard deviation was $6050. At the α=0.01, is there sufficient evidence to conclude that the cost of attendance has increased?

Step-by-step explanation:

1)

Mean = (112 + 120 + 98 + 55 + 71 + 35 + 99 + 124 + 64 + 150 + 150 + 55 + 100 + 132 + 20 + 70 + 93)/17 = 91.1

Standard deviation = √(summation(x - mean)/n

Summation(x - mean) = (112 - 91.1)^2 + (120 - 91.1)^2 + (98 - 91.1)^2 + (55 - 91.1)^2 + (71 - 91.1)^2 + (35 - 91.1)^2 + (99 - 91.1)^2 + (124 - 91.1)^2 + (64 - 91.1)^2 + (150 - 91.1)^2 + (150 - 91.1)^2 + (55 - 91.1)^2 + (100 - 91.1)^2 + (132 - 91.1)^2 + (20 - 91.1)^2 + (70 - 91.1)^2 + (93 - 91.1)^2 = 23550.97

s = √23550.97/17 = 37.2

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 37.2

n = number of samples = 17

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.12

Margin of error = 2.12 × 37.2/√17

= 19.13

The 95% confidence interval for the hemoglobin reading for all the patients in the hospital is

91.1 ± 19.13

2) Confidence interval for population proportion is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 500

x = 60

p = 60/500 = 0.12

q = 1 - 0.12 = 0.88

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 1.645. Thus, Tthe z score for a confidence level of 90% is 1.645

Therefore, the 90% confidence interval is

0.12 ± 1.645√(0.12)(0.88)/500

Confidence interval = 0.12 ± 0.024

3) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 19410

For the alternative hypothesis,

µ > 19410

This is a right tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 19410

x = 22098

σ = 6050

n = 40

z = (19410 - 22098)/(6050/√40) = - 2.81

Looking at the normal distribution table, the probability corresponding to the z score is 0.0025

p value = 0.0025

Since alpha, 0.01 > than the p value, 0.0025, then we would reject the null hypothesis. Therefore, At a 1% level of significance, there is sufficient evidence to conclude that the cost of attendance has increased.

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all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

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