Question

. A magazine claimed that less than 1 out of 3 Americans were
single. A random sample of Americans were asked their marital status. Use α=0.05.
M S M M S W W D M D D S D M
M S M D M M S D M M S M M M
S M M W D W M M M S M S M M
W S D S M M M M

b) What is the p-value?
c) Type in your hypotheses using correct notation.
d) Type in your decision.
e) Type in your conclusion using context and units from the problem

Answer 1

The hypothesis being tested is:

H₀: p = 1/3 = 0.33

H_a: p < 0.33

n = 50

p̂ = 11/50 = 0.22

The test statistic, z = (p̂ - p)/√p(1-p)/n

z =  

z = -1.70

The p-value for z = -1.70 is 0.0446.

Since the p-value (0.0446) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that less than 1 out of 3 Americans were single.

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