A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 380 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 380 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey? Attitude 1st Survey 2nd Survey

Optimistic 6% 1%

Slightly Optimistic 29% 30%

Slightly Pessimistic 24% 28%

Pessimistic 41% 41%

Find the value of the test statistic. Round your answer to three decimal places.

The null and alternative hypotheses:

H0: attitudes between first survey and second survey have not changed.

H1:attitudes between first survey and second survey have changed.

Let's find the observed and expected value using the following:

Observed value = sample size * observed proportion

Expected value = sample size * expected proportion.

Optimistic:

expected= 6%*380=22.8

observed=1%*380=3.8  

(fo-fe)²/fe = 15.83333

Slightly Optimistic:

expected: 29%*380=110.2);

Observed: 30%*380= 114

(fo-fe)²/fe  = 0.131034

Slightly Pessimistic:

expected= 24%*380= 91.2

Observed = 28%*380=106.4  

(fo-fe)²/fe =  2.533333

Pessimistic:

Expected = 41%*380 =155.8

Observed = 41%*380 =155.8

(fo-fe)²/fe = 0

Total (fo-fe)²/fe =

15.83333 + 0.131034 + 2.533333 + 0 = 18.4977

Degrees of freedom, df = 4 - 1 = 3

For chi square test statistic:

Σ(fo-fe)²/fe = 15.83333 + 0.131034 + 2.533333 + 0 =  18.498

Calculate pvalue.

Calculating for pvalue at, df = 3, chi-square score = 18.4977, α=0.05

Pvalue = 0.000347

Decision:

Since pvalue, 0.000347 is less than significance level, 0.05, reject null hypothesis H0.

Conclusion:

There is enough evidence to conclude that there is a change in attitudes between  first survey and the second survey at a level of significance, 0.05.

idk

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."