Question

with the new dough, there were 16 complaints out of 340 pizzas. let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. based on a 95% confidence for the difference of the proportions, what can be concluded?

Answer 1

The correct answer is:

Reject null hypothesis H0, we cannot conclude the proportion of customer complaints is more for the old dough.

As given in the question,

Let us consider proportion of customer complaints with old dough is p₁

And proportion of complaints with new dough is p₂

Difference in proportion of complaints in old and new dough

= p₁ - p₂

Null hypothesis : H0 : p1 ≥ p2

p₁ - p₂  ≥ 0

Alternative hypothesis : Ha : p1 < p2

p1 - p2 < 0

Let 'x' represents the number of complaints

Sample size = n

Sample proportion = x/n

Old dough:

Number of complains with old dough 'x₁' = 6

Number of pizzas with old dough 'n₁' = 385

p₁ = 6/385

   = 0.01558

   = 0.016

New dough:

Number of complains with new dough 'x₂' = 16

Number of pizzas with new dough 'n₂' = 340

p₂ = 16/340

   = 0.04705

   = 0.047

Pooled proportion test:

$\bar{p}$ = (x₁+ x₂)/(n₁ + n₂)

  = (6 + 16)/(385 + 340)

  = 0.0303

  = 0.03

1 -  $\bar{p}$ = 1 - 0.03

      = 0.97

z = (p₁ - p₂)/√$\bar{p}$(1 - $\bar{p}$)(1/n₁ + 1/n₂)

 = (0.016 - 0.047)/√(0.03)(0.97)(1/385 + 1/340)

 = (-0.031)/ √(0.03)(0.97)(0.0026 + 0.0029)

 = - 0.031/√0.00016005

 = -0.031 / .01265

 = -2.45

It is left tailed test.

p value for the area to the left of the z score using normal distribution table:

p value = 0.007143

Significant level 'α' for  95% confidence level:

= 1 - 0.95

= 0.05

Since 0.05 > 0.0.007143

Reject null hypothesis.

Therefore, reject H0, we cannot conclude the proportion of customer complaints is more for the old dough.

The complete question is :

Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. Based on a 95% confidence for the difference of the proportions, what can be concluded?

Multiple Choice

A. Reject H0, we can conclude the proportion of customer complaints is more for the old dough

B. Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

C. Do not reject H0, we can conclude the proportion of customer complaints is more for the old dough

D. Reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

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