Question

A national survey conducted in 2011 among a simple random sample of 1,507 adults shows that 56% of americans think the civil war is still relevant to american politics and political life. conduct a hypothesis test at significance level α=0.05 to determine whether these data provide strong evidence that a majority of american adults think the civil war is still relevant.

Answer 1

Answer:

Null : x = 0.56 ; Alternate : x < 0.56

t = (x - 0.56) / (s / √n) : If < tabulated t at α =0.05 , null hypothesis  accepted

If t > tabulated t at α =0.05 , alternate hypothesis is accepted

Explanation:

Hypothesis Testing is used to test the statistical validity of a statement. Null Hypothesis is the neutral hypothesis, signifying equality to the tested value. Alternate Hypothesis is the contradictory hypothesis, signifying deviation from the tested value.

To test 'Proportion of people giving importance to civil rights in american political life' : Let these proportion be = x

Null Hypothesis (H0) : x = 56% = 0.56

Alternate Hypothesis (H1) : x < 56 % , i.e x < 0.56

't' statistic is calculated based on sample : ( x' - u ) / (s / √n)

where : x' = sample mean , u = population hypothesised mean = 0.56 , s = sample standard deviation , n = sample size

If this calculated 't' < tabulated 't' at significance level α =0.05 ; null hypothesis is accepted. It implies average people thinking as mentioned = 56 % (majority)

If this calculated 't' > tabulated 't' at significance level α =0.05 ; alternate hypothesis is accepted. It implies average people thinking as mentioned < 56% (not majority)