Question

6. As the contributions of money from state and local governments to public school sys- tems has decreased school systems have become more dependent on raising money through the ballot with millages. The biggest roadblock to these efforts is resistance from the public (and, all too often, outside groups who don't have any local interest in the schools). One local school system tried to get millage passed in 2016, but opposition of 52% of the area residents prevented its passage Since then school officials have been working to give better explanations of the need for the millage: school buildings that are over fifty years old are in need of repair, HVAC systems need to be repaired or replaced, and so on. The hope is that these explanations will reduce the level of opposition. A new survey, done in 2017, included 2200 households with school-aged children. It was found that 1037 households still opposed the millage. You'll use this data to test whether the level of opposition has decreased since 2016. (a) (4 points) What null and alternative hypotheses should be tested? (b) (8 points) Use the information from the problem and Minitab to perform the test using a 0.05. What is the conclusion? 7. (5 points) After she read that the national average amount spent on dinner by couples celebrating their first anniversary was $120, a restauranteur's reaction was "That seems too low. She took a random sample of 20 receipts for dinners shed hosted and could confirm were first anniversary dinners for her clients. Table 2 shows the data. TABLE 2: DINNEr RECEIPTS, IN DOlLaRs, FOR 20 RANDOMLY SE- LECTED FIRST ANNIVERSARY DINNERS 149 122 139119 136 129 133 140 126 128 Use this data (type it into a single Minitab column) to test whether the mean cost of a first anniversary dinner form this restauranteur is higher than S120. Write out the hypotheses to test, include the Minitab output, and give the interpretation.

Answer 1

6)

a)

Test

Null hypothesis	H₀: p = 0.52
Alternative hypothesis	H₁: p < 0.52

mini tab results

b)

Test and CI for One Proportion

Method

p: event proportion

Normal approximation method is used for this analysis.

Descriptive Statistics

N	Event	Sample p	95% Upper Bound for p
2200	1163	0.528636	0.546142

Test

Z-Value	P-Value
0.81	0.791

Since the p-value of this test is more than 0.05 (level of significance) we fail to reject null hypothesis. We conclude that there is no significant evidence that level of proportion has been decreased from 2016.

7)

One-Sample T: Cost of a first anniversary dinner.

Descriptive Statistics

N	Mean	StDev	SE Mean	95% Lower Bound for μ
20	130.10	9.97	2.23	126.24

μ: mean of Cost of a first anniversary dinner.

Test

Null hypothesis	H₀: μ = 120
Alternative hypothesis	H₁: μ > 120

T-Value	P-Value
4.53	0.000

Since p-value is less that 0.05 we reject null hypothesis, there is a significant evidence to conclude that mean Cost of a first anniversary dinner is greater than $120.