Question

during the fall of 2000-2001, the average bill for California residents was $186 per month. A random sample of 40 customers were selected during the fall of 2001-2002, and the average bill was found to be $178.10 with a sample standard deviation of $22.40. Using alpha equals .05, does this sample provide enough evidence to conclude that the average utility bill in California was lower in the fall of 2001-2002 than it was in the fall of 2000-2001?

Q 1)what is the correct calculation value for this testing scenario?

a)-2.23

b)1.69

c)-1.69

d)2.23

Q2) what is the correct critical value for this scenario?

a) 2.23

b)1.69

c)-2.23

d)3.54

Q3) what is the correct decision in report for this scenario (hypothesis test, ex fail to reject Ho, Reject Ho, etc)

please answer all parts of the question I will thumbs up for correct answer with a timely response.

thanks

Answer 1

Ho: = 186

Ha: < 186

Null hypothesis states that  average utility bill in California in the fall of 2001-2002 is equal to 186

Alternative hypothesis states that  average utility bill in California in the fall of 2001-2002 is less than 186

Test statistics

n = 40

sample mean = 178.10

sample sd = 22.40

Assuming that data is normally distrbuted, also as the population sd is not given, we will calculate t stat

Q 1) t stat = - 2.23

t critical for df = 39, level of significance = 0.05 = - 1.685

Q 2) t critical =  - 1.69

Q 3) As the t stat falls in the rejection area, we reject the Null hypothesis. Reject Ho

Hence we have sufficient evidence to believe that average utility bill in California in the fall of 2001-2002 is less than 186.