Hypothesis Testing for Proportions

I started these but am not sure how to finish them, any help would be appreciated.(Headbang)

1. Use the method specified to perform the hypothesis test for the population mean m. A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 6 years. A sample of 80 convicted car thieves was randomly selected. The mean of the sample was found to be 5.5 years. The population standard deviation is known to be 1.25 years. At a = 0.05, test the politician’s claim

a. **Use the critical value z0 method** from the normal distribution.

**1. ****H0 : µ ≥ 6**

**Ha : µ < 6**

**2. ****a**** = 0.05**

**3. ****Test statistics: left-tailed**

**4. ****P-value or critical z0 or t0. -1.645**

**5. ****Rejection Region: z < -1.645**

**6. ****Decision: 6-5.5 = 0.5/1.25√80 =-3.58**

**7. ****Interpretation: There is not enough evidence at the 5% level of significance to support the local politician’s claim that the mean prison time for car thieves is less than 6.**

b. **Use the P-value method. **

**1. ****H0 : **

**Ha : **

**2. ****a**** = **

**3. ****Test statistics: **

**4. ****P-value or critical z0 or t0. **

**5. ****Rejection Region:**

**6. ****Decision:**

7. **Interpretation: **

Question 2

**Hypothesis Testing for Proportions.**

The engineering school at a Northern university claims that 20% of its graduates are women. In a graduating class of 210 students, 58 were women. Does this suggest that the school is believable? Use a level of significance of a = 0.05 to test the school’s claim. Use an alternative hypothesis of p ¹ 0.2 (Round phat to 4 decimal places.)

**1. ****H0 : p≥0.2**

**Ha : p<0.2**

**2. ****a**** = 0.05**

**3. ****Test statistics: 2.76 0.42-0.2/(0.2)(0.8)/210=0.95**

**4. ****P-value or critical z0 or t0. **

**5. ****Rejection Region: **

**6. ****Decision: **

**7. ****Interpretation: **