Stating Hypotheses
State the null and alternative hypotheses in symbolic form.
Claim: 60% of people are allergic to dairy products.
H0: p = 0.60
H1: p ≠ 0.60
In testing H0: p = 0.52, H1: p > 0.52 at a level of significance of 0.05, a p-value of 0.0356 was found. State a decision about the null hypothesis.
Reject H0
To test the claim that the mean weight of male standard poodles is greater than 60 lbs, the following information was determined:
H0: µ = 60, H1: µ > 60
α = 0.05, p-value = 0.00004, Reject H0
State the conclusion in non-technical terms.
There is sufficient evidence to support the claim that the mean weight of male standard poodles is greater that 60 lbs.
Using 1-PropZTest, find the test statistic and p-value for the following data:
H0: p = 0.50, H1: p > 0.50, x = 37, n = 66
Test Stat z = 0.9847
p-value = 0.1624
H0: p ≤ 0.674
H1: p > 0.674
Error: H0: p ≤ 0.674
The null hypothesis must contain an equal sign.
Correction: H0: p = 0.674
State the null and alternative hypotheses in symbolic form.
Claim: At least 91% of drivers wear their seatbelts.
H0: p = 0.91
H1: p < 0.91
In testing H0: µ = 36, H1: µ ≠ 36 at a level of significance of 0.05, a p-value of 0.0711 was found. State a decision about the null hypothesis.
Fail to reject H0
To test a juice company’s claim that their bottles have a mean amount of juice of 15 oz, the following information was determined:
H0: µ = 15, H1: µ ≠ 15
α = 0.05, p-value = 0.2247, Fail to Reject H0
State the conclusion in non-technical terms.
There is not sufficient evidence to warrant rejection of the claim that the mean amount of juice is 15 oz.
Using 1-PropZTest, find the test statistic and p-value for the following data:
H0: p = 0.12, H1: p ≠ 0.12, x = 122, n = 401
Test Stat z = 11.3533
p-value = 7.33 x 10-30 = 0
H0: x-bar = 42.8
H1: x-bar ≠ 42.8
Error: hypotheses must contain parameters, not statistics.
Correction:
H0: µ = 42.8
H1: µ ≠ 42.8
State the null and alternative hypotheses in symbolic form.
Claim: The average height of women is at most 163 cm.
H0: µ = 163
H1: µ > 163
It is believed that among all births, the proportion of boys is 0.512. The p-value to test this claim was found to be 0.3286. At α = 0.01, state a decision about the null hypothesis.
H0: p = 0.512, H1: p ≠ 0.512
Fail to reject H0
A building company claims that more than 70% of new homes being built contain 3 bathrooms. To test this claim the following information was determined:
H0: p = 0.70, H1: p > 0.70
α = 0.10, p-value = 0.3781, Fail to Reject H0
State the conclusion in non-technical terms.
There is not sufficient evidence to support the claim that more than 70% of new homes contain 3 bathrooms.
Using 1-PropZTest, find the test statistic and p-value for the following data:
H0: p = 0.74, H1: p < 0.74, x = 68, n = 100
Test stat z = -1.3679
p-value = 0.0857
H0: p = 0.25
H1: p > 0.31
Error: hypotheses must use the same value.
Correction:
H0: p = 0.25
H1: p > 0.25
State the null and alternative hypotheses in symbolic form.
Claim: The mean lifespan of a certain lightbulb is more than 600 hours.
H0: µ = 600
H1: µ > 600
A physician claims that the average resting heart rate for adults should be 72 beats per minute. To test this claim a p-value of 0.0219 was calculated. At α = 0.01, state a decision about the null hypothesis.
H0: µ = 72, H1: µ ≠ 72
Fail to reject H0
To test the claim that the proportion of girls in all births is 0.488, the following information was determined:
H0: p = 0.488, H1: p ≠ 0.488
α = 0.01, p-value = 0.0064, Reject H0
State the conclusion in non-technical terms.
There is sufficient evidence to warrant rejection of the claim that the proportion of girls in all births is 0.488.
Using 1-PropZTest, find the test statistic and p-value for the following data:
H0: p = 0.33, H1: p > 0.33, n = 265, p-hat = 35%
(x = 93)
Test Stat z = 0.7251
p-value = 0.2342
H0: p = 0.89
H1: p > 0.89
α = 0.05, p-value = 0.0478, Fail to reject H0
Error: incorrect decision. The p-value is less than alpha.
Correction: Reject H0
State the null and alternative hypotheses in symbolic form.
Claim: The average time to complete a statistics exam is equal to 35 minutes.
H0: µ = 35
H1: µ ≠ 35
A news article claims that more than 75% of households have a TV in their kitchen. To test this claim a p-value of 0.0008 was calculated. At α = 0.10, state a decision about the null hypothesis.
H0: p = 0.75, H1: p > 0.75
Reject H0
To test the claim that the mean human body temperature is equal to 98.6°F, the following information was determined:
H0: µ = 98.6, H1: µ ≠ 98.6
α = 0.01, p-value = 0.0002, Reject H0
State the conclusion in non-technical terms.
There is sufficient evidence to warrant rejection of the claim that the mean human body temperature is equal to 98.6°F.
Using 1-PropZTest, find the test statistic and p-value for the following data:
H0: p = 0.60, H1: p ≠ 0.60, n = 568, p-hat = 52%
(x = 295)
Test stat z = -3.9227
p-value = 8.8 x 10-5 = 0.00008
H0: µ ≠ 500
H1: µ = 500
α = 0.05, p-value = 0.1447, Fail to reject H0
Error: incorrect hypotheses. The equal sign must be in the null hypothesis.
Correction:
H0: µ = 500
H1: µ ≠ 500