Question

1.) Suppose when an automobile is painted prior to final assembly the resulting paint job is considered acceptable 78% of the time. In a random sample of 250 autos, it was found that 202 had acceptable quality paintwork. Perform a complete test of hypotheses to determine if the original assumption (78%) seems reasonable.
2.) Suppose a random sample of 4 100 watt bulbs resulted in the following observations of lumens: 1612, 1597, 1611, 1614. Knowing the true standard deviation in the lumen output is 59 Run a formal test of hypotheses to determine if the output of the bulbs is significantly higher than 1580 lumens.

One-Sample Z: Lumens

Test of u = 1580 vs > 1580

The assumed standard deviation = 59

Variable N Mean StDev SE Mean 95% Lower Bound Z P

Lumens 4 1608.5 7.8 29.5 1560.0 0.97 0.167

3.) A comparison was made in the interest of determining if Oreo Double Stuf cookies really have double the amount of filling as a standard Oreo cookie. If we may assume that the traditional Oreo cookie has 3 g of "stuf" use a 1% level of significance to determine if the cookies are made correctly.

Descriptive Statistics: Double Stuf
Variable Total-Count Mean StDev

Double Stuf 79 6.1575 0.2957

4.) Suppose in a random sample of 120 Li-ion batteries 36 are found to be defective. The next month, the second sample of 143 batteries found that 58 are defective. Based on these results, perform a complete test to determine if there has there been an increase in the rate of defects in the next month.

Answer 1

(1)

H0: Null Hypothesis: P = 0.78 ( the original assumption (78%) seems reasonable. ) (Claim)

HA: Alternative Hypothesis: P 0.78 ( the original assumption (78%) does not seem reasonable. )

n = 250

= 202/250 = 0.808

Take = 0.05

From Table, critical values of Z = 1.96

Test Statistic is given by:

Since calculated value of Z = 1.069 is less than critical value of Z= 1.96, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data support the claim that the original assumption (78%) seems reasonable.

(2)

H0: Null Hypothesis: 1580 ( the output of the bulbs is not significantly higher than 1580 lumens )

HA: Alternative Hypothesis: > 1580 ( the output of the bulbs is significantly higher than 1580 lumens ) (Claim)

n = 4

= 1608.5

= 59

Take = 0.05

From Table, critical value of Z = 1.64

Test Statistic is given by:

Since calculated value of Z = 0.966 is less than critical value of Z = 1.96, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the output of the bulbs is significantly higher than 1580 lumens.

(3)

H0: Null Hypothesis: = 6 ( Oreo Double Stuf cookies really have double the amount of filling as a standard Oreo cookie. ) (Claim)

HA: Alternative Hypothesis: 6 ( Oreo Double Stuf cookies really do not have double the amount of filling as a standard Oreo cookie. )

n = 79

= 6.1575

s = 0.2957

= 0.01

df = 79 - 1 = 78

From Table, critical values of t = 2.64

Test Statistic is given by:

Since calculated value of Z = 4.734 is greater than critical value of Z = 2.64, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that Oreo Double Stuf cookies really have double the amount of filling as a standard Oreo cookie.

(4)

H0: Null Hypothesis: p1 p2 ( there has not been an increase in the rate of defects in the next month )

HA: Alternative Hypothesis: p1 < p2 ( there has been an increase in the rate of defects in the next month ) (Claim)

n1 = 120

1 = 36/120 = 0.3

n2 = 143

2 = 58/143 = 0.4056

= 0.05

From Table, critical value of Z = - 1.64

Pooled Proportion is given by:

Test Statistic is given by:

Since calculated value of Z =- 1.78 is less than criticalvalue of Z = - 1.64, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there has been an increase in the rate of defects in the next month.