question archive 7) Bonnie and Katie buy some Better Burner brand microwave popcorn in the 25-bag Extra Value Pack
7) Bonnie and Katie buy some Better Burner brand microwave popcorn in the 25-bag Extra Value Pack
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7) Bonnie and Katie buy some Better Burner brand microwave popcorn in the 25-bag Extra Value Pack. This brand claims perfect popcorn with a mean popping time of 4 minutes, and cites studies which show that all brands of microwave popcorn have normally distributed popping times with standard deviation σ = 0.7 minutes. Before sampling the 25 bags of popcorn themselves, they pop all 25 bags in their sample and compute a mean popping time = 3.7 minutes.
Is this significant evidence that the true mean popping time really is different from (not equal to) 4 minutes?
Set up appropriate null and alternative hypotheses, calculate the appropriate test statistic, find the P-value, and state your conclusion (use α = .05).
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According to the question,
Given data are:
x? = 3.7
σ = 0.7
n = 25
Hypothesis:
H0 : μ = 4
H1 : μ ≠ 4
The test statistic is:
Z = (x? - μ) / (σ / √n)
= (3.7 - 4) / (0.7 √25)
= -2.143
p-value is:
= 2 * P(z < -2.143)
= 2 * 0.016057 [ in any blank cell of excel type =NORMSDIST(-2.143)]
≈ 0.0321
decision:
p value = 0.0321 < 0.05 (Alpha)
so, we reject the null hypothesis.
conclusion:-
There is significant evidence that the true mean popping time really is different from (not equal to) 4 minutes.
