(For Questions 1 & 2) UMUC Stats Club conducted an online poll of 500 adults in

Question

(For Questions 1 & 2) UMUC Stats Club conducted an online poll of 500 adults in May 2017. One question was “Do you believe that the climate change is due to global warming?”. Out of the 500 adults, 420 adults answered “Yes”.

1. Find a 90% confidence interval estimate of population proportion of adults who support the claim that climate change is due to global warming. (Explain how you get the critical value, show work and round the answer to three decimal places)

2. In a similar online poll conducted in 2016, 80% of adults supported the claim. In order to determine if the proportion of adults who support the claim in 2017 is higher than one year ago, we would like to perform the following hypothesis test:

H_0: p=0.80

H_a: p>0.80

(a) Find the test statistic. (Show work and round the answer to two decimal places)

(b) Determine the P-value for this test. (Show work and round the answer to three decimal places. If you use technology to find the P-value, you have to describe the steps)

(c) Is there sufficient evidence to justify the rejection of at the =0.05 level? Explain.

Explanation / Answer

1) here sample proportion phat =420/500 =0.84 ; and n=500

therefore std error =(phat(1-phat)/n)1/2 =0.0164

for 90% confidence interval; z =1.645 ( from excel function --normsinv(0.95) =1.645; revert if yu are using some other mode)

therfore 90% confidence interval estimate of population proportion = phat -/+ z*std error =0.8130 to 0.8670

2) here std error =(p(1-p)/n)1/2 whwere p=0.80 and n=500

=0.0179

therefore test statistic z =(phat-p)/std error =(0.84-0.80)/0.0179 =2.2361

b) p value for above test statistic =0.0127 ( from excel function = 1-normsdist(2.2361)

c) as p value is less then 0.05 level we can reject null hypothesis

there is sufficient evidence to justify the rejection of at the =0.05 level

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