Can you determine what number x represents from the information given? explain how you got your answer.

Sample response: Yes, you can determine the number of people who do not run or lift weights by first finding that 55 people do not lift weights, and that 35 people run, but do not lift weights. Subtracting 35 from 55, you get that 20 people do not do either.

x = 25

Step-by-step explanation:

75 (total amount of people that run) minus 40 (amount of people that lift weights and run) equals 35 (amount of people that run but don't lift weights)

120 (total amount of people surveyed) minus 65 (total amount of people that lift weights) equals 55 (total amount of people that do not lift weights)

55 (total amount of people that do not lift weights) minus 35 (total amount of people that run but don't lift weights) equals 25 (total amount of people that don't run or lift weights.

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.