Formulate the null and alternative hypothesis of the given problem.

1.)The principal of a certain high school claims that 85% of all the students is in

favor of the new school uniform. A Statistics teacher asked his students to

verify the claim. Suppose that 451 out of the 550 randomly selected

students indicated that they are in favor of the new school uniform. At 0.05

level of confidence, is there enough evidence to conclude that the

percentage of students who are in favor of the new uniform is different from

85%?

Task B: Answer the ff:

Electrolux Incorporated manufactures and sells home products for the last

25 years. They claim that their vacuum cleaner disburse a mean of 46 kilowatt

hour/year. In a survey conducted by business students, 12 homes were asked and

responses indicated that vacuum cleaners produced by Electrolux disburse a mean

of 42 kilowatt hour per year with a standard deviation of 11.9 kilowatt-hours. Can

we conclude at the 0.05 level of significance that Electrolux vacuum cleaners

disburse, on the average, less than 46 kilowatt-hours per year? Assume the

population of kilowatt-hours to be approximately normal.

FOLLOW THE FORMAT IN ANSWERING. (If there are any errors, feel free to correct it. show your solutions. Thanksssssssssssss)))

Given: n=12 X=42 $=11.9 # =46 0=0.05 STEPS SOLUTIONS STEP 1: Formulate the null and alternative hypothesis. STEP 2: Specify the level of significance. a = 0.05 One tailed to the left STEP 3: Choose the appropriate test statistic. NOTE: (The number of samples is 12 and 12 is less than 30) STEP 4: Establish the critical region. t critical values: -2.201 STEP 5: Compute for the value of the test statistic. STEP 6: Make a decision and interpret the result. 1.10 >-2.201 The null hypothesis is failed to reject. So, there is no significant difference between the sample mean and the population mean. Therefore, the claim is true