Question

1. Conduct a test of the hypothesis that the mean climate sentiment score is different than 33.8 (the climate sentiment score from last quarter’s Stat 220). Be sure to state your statistical hypotheses using symbols, report the p-value, report the decision of your test, and provide a conclusion in the context of the problem. Use a 5% significance level.

z=2.9389

p-value=0.003294

Alternative hypothesis: the true mean not equal to 33.8

For a 95% confidence interval: 34.15060 to 35.55453

Sample estimates: mean of x= 34.85256

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: The mean climate sentiment score is 33.8.

Alternative hypothesis: Ha: The mean climate sentiment score is different than 33.8.

H0: µ = 33.8 versus Ha: µ ≠ 33.8

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

Z = 2.9389

P-value = 0.003294

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

Also, the given confidence interval does not contain the value 33.8, so we reject the null hypothesis.

Conclusion:

There is sufficient evidence to conclude that the mean climate sentiment score is different than 33.8.