Question

According to​ research, holiday shoppers spent an average of

​$366

over a holiday weekend in 2008. The accompanying data show the amount spent by a random sample of holiday shoppers during the same weekend in 2009. Complete parts a and b below.

$421	​$278	​$376	​$232	​$221	​$219
​$358	​$433	​$388	​$391	​$328	​$65
​$414	​$434	​$376	​$270

critical values?

Test statistic?

What is the conclusion?

P-value?

Answer 1

Answer: According to​ research, holiday shoppers spent an average of ​$366 over a holiday weekend in 2008. The accompanying data show the amount spent by a random sample of holiday shoppers during the same weekend in 2009.

Solution:

The hypothesis test:

Null hypothesis, Ho: μ ≥ 366

Alternative hypothesis, Ha: μ < 366

Mean, x̄ = Σx/n

Mean, x̄ = 5204/16

Mean, x̄ = 325.25

S.D, s = √Σ(xi - x̄)^2/n-1

s = √Σ(xi - 325.25)^2/16-1

s = √158841/15

S.D, s= 102.9048

Test statistic t:

t = x̄ - μ / s / √n

t = 325.25 - 366 / 102.9048 / √16

Test statistic t = - 1.5839

t critical :

Assuming significance level α = 0.05

df = n-1 = 16 - 1 = 15

t critical = t(α,df) = t(0.05,15)

t critical = 1.7530

Conclusion:

Since, test statistic t (-1.584) > t critical (-1.753)

Do not reject the null hypothesis Ho.

There is insufficient evidence to conclude that holdiay shoppers spent, an average amount spent by a random sample of holiday shoppers during the same weekend in 2009.

P-value:

P-value from test statistic and df at α = 0.05 significance level:

P-value = 0.067023

Since, P-value (0.067) > α (0.05) significance level.

Do not reject the null hypothesis Ho.