for Prof Double R

μ ≤ 940.36 + (1.645)(62.2/(60)½)

μ ≤ 953.576

We are 95% confident that the mean death will be less than 953.57.

99% CI on the population mean fe death rate:

1-.99=𝜶=0.01

μ ≤ 940.36 + (2.575)(62.2/(60)½)

μ ≤ 961.04

We are 99% confident that the mean death rate will be less than 961.04

We note that with a larger level of confidence the confidence interval range is also larger.

Hypothesis Testing: (using the p-value approach)

H0: μ = 920

H1: μ = 920

*one-sided hypothesis testing* * use t-distribution because….

Test statistic: t0 = (x̄ - μ)/ (s/(n)1/2 )

=(940.36 - 920)/ (62.2/(60)½)

= 2.535496

2.390 < tp, 59 < 2.660

0.01 < P < 0.005

For confidence level 90% → 𝜶=0.1

Since tp, 59 falls between the two values: 2.390, for which 𝜶=0.01, and 2.660, for which 𝜶=0.005, we can say that the one-tailed test has a p -value between those two values. That is 0.005<P<0.01. Therefore P< 𝜶= 0.1 and hence we reject the H0 and conclude thats the mean death rate is less than 920.

2-2 Random sample of size 25 of death rate:

H0: μ=920 H1: μ<920 → One Sided Test

1. 90% Confidence Interval on the population mean:

1-ɑ=.9 , ɑ=.1, z𝜶 =Z0.1=1.28

Sample size=25

Sample mean=938.6

Sample standard deviation=65.06274 (known→z distribution)

μ ≤ x̄ + z𝜶(σ/(n)1/2 )

μ≤938.6+1.28(65.06274/√25)

μ≤955.256

We are 90% confident that the mean death rate is less than 955.256

2. 99% Confidence Interval on the population mean:

1-ɑ=.99, ɑ=.01, z𝜶 =Z0.01=2.33

μ ≤ x̄ + z𝜶(σ/(n)1/2 )

μ≤938.6+2.33(65.06274/√25)

μ≤968.919

We are 99% confident that the mean death rate is less than 968.919

3. 1. Parameter of Interest: population mean

2. H0: μ=920

3. H1: μ<920 → One Sided Hypothesis test

4. Test statistic: (x̄-μ)/(σ/√n)

5. Rejection Criteria: P-value<⍺

6. z0=(938.6-920)/(65.06274/√25)=0.5717

P-value=P(x̄<z0)=P((x̄-μ)/(σ/√n)<0.5717)=P (Z<0.5717)=.7517

7. P-value=0.7517→P-value⩻⍺→0.7517⩻⍺→No→Accept the Null Hypothesis

Didn’t meet the rejection criteria=>Accept the Null Hypothesis

2-3

n=60

Variable: A1

x̄=37.37, σ=9.98

H0:μ=31.7 H1:μ≠31.7

P-value=P(x̄>37.37)+P(x̄<26.03) z0=(x̄-μ)/(σ/√n)=(37.37-31.7)/(9.98/√60)=4.401→z0=±4.401