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The head start program provides a wide range of services to low-income children up to the...

The head start program provides a wide range of services to low-income children up to the age of 5 years and their families. Its goals are to provide services to improve social and learning skills and to improve health and nutrition status so that the participants can begin school on an equal footing with their more advantaged peers. The distribution of ages for participating children is as follows 12% five-year-olds, 47% four-year-olds, 33% three-year-olds, and 8% under three years. When the program was assessed in a particular region, it was found that of the 215 randomly selected participants, 17 were 5 years old, 101 were 4 years old, 60 were 3 years old, 37 were under 3 years old. Perform a test to see if there sufficient evidence at αα = 0.10 that the region's proportions differ from the national proportions.

The correct hypotheses are:

  • H0:H0: The regional distribution is a good fit to the national distribution. HA:HA: The regional distribution is not a good fit to the national distribution.(claim)
  • H0:H0: The regional distribution is not a good fit to the national distribution. HA:HA: The regional distribution is a good fit to the national distribution.(claim)
  • H0:H0: The regional distribution and the national distribution are independent. HA:HA: The regional distribution and the national distribution are dependent.(claim)
  • H0:H0: The regional distribution and the national distribution are dependent. HA:HA: The regional distribution and the national distribution are independent.(claim)

The test value is (round to 3 decimal places)

The p-value is (round to 3 decimal places)

According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:

Action % of time
On Time 71
National Aviation System Delay 8
Aircraft arriving late 8
Other (weather and other conditions) 13

When a study was conducted it was found that of the 250 randomly selected flights, 180 were on time, 18 were a National Aviation System Delay, 20 arriving late , 32 were due to weather. Perform a test to see if there is sufficient evidence at αα = 0.05 to see if these differ from the governments statistics.

The correct hypotheses are:

  • H0:H0: The sample is a good fit to the Bureau of Transportation Statistics. HA:HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim)
  • H0:H0: The sample is not a good fit to the Bureau of Transportation Statistics. HA:HA: The sample is a good fit to the Bureau of Transportation Statistics.(claim)
  • H0:H0: The sample and the Bureau of Transportation Statistics are independent. HA:HA: The sample and the Bureau of Transportation Statistics are dependent.(claim)
  • H0:H0: The sample and the Bureau of Transportation Statistics are dependent. HA:HA: The sample and the Bureau of Transportation Statistics are independent.(claim)

The test value is  (round to 3 decimal places)

The p-value is (round to 3 decimal places)

The head start program provides a wide range of services to low-income children up to the age of 5 years and their families. Its goals are to provide services to improve social and learning skills and to improve health and nutrition status so that the participants can begin school on an equal footing with their more advantaged peers. The distribution of ages for participating children is as follows 10% five-year-olds, 50% four-year-olds, 28% three-year-olds, and 12% under three years. When the program was assessed in a particular region, it was found that of the 202 randomly selected participants, 20 were 5 years old, 99 were 4 years old, 46 were 3 years old, 37 were under 3 years old. Perform a test to see if there sufficient evidence at αα = 0.01 that the region's proportions differ from the national proportions.

The correct hypotheses are:

  • H0:H0: The regional distribution is a good fit to the national distribution. HA:HA: The regional distribution is not a good fit to the national distribution.(claim)
  • H0:H0: The regional distribution is not a good fit to the national distribution. HA:HA: The regional distribution is a good fit to the national distribution.(claim)
  • H0:H0: The regional distribution and the national distribution are independent. HA:HA: The regional distribution and the national distribution are dependent.(claim)
  • H0:H0: The regional distribution and the national distribution are dependent. HA:HA: The regional distribution and the national distribution are independent.(claim)

The test value is (round to 3 decimal places)

The p-value is (round to 3 decimal places)

According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:

Action % of time
On Time 68
National Aviation System Delay 7
Aircraft arriving late 8
Other (weather and other conditions) 17

When a study was conducted it was found that of the 230 randomly selected flights, 159 were on time, 21 were a National Aviation System Delay, 21 arriving late , 29 were due to weather. Perform a test to see if there is sufficient evidence at αα = 0.01 to see if these differ from the governments statistics.

The correct hypotheses are:

  • H0:H0: The sample is a good fit to the Bureau of Transportation Statistics. HA:HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim)
  • H0:H0: The sample is not a good fit to the Bureau of Transportation Statistics. HA:HA: The sample is a good fit to the Bureau of Transportation Statistics.(claim)
  • H0:H0: The sample and the Bureau of Transportation Statistics are independent. HA:HA: The sample and the Bureau of Transportation Statistics are dependent.(claim)
  • H0:H0: The sample and the Bureau of Transportation Statistics are dependent. HA:HA: The sample and the Bureau of Transportation Statistics are independent.(claim)

The test value is (round to 3 decimal places)

The p-value is (round to 3 decimal places)

Solutions

Expert Solution

Question 1:

AGE Observed Frequency (O) Expected Frequency (E) (O-E)²/E
5 Years 17 215 * 0.12 = 25.8 (17 - 25.8)²/25.8 = 3.0016
4 Years 101 215 * 0.47 = 101.05 (101 - 101.05)²/101.05 = 0
3 Years 60 215 * 0.33 = 70.95 (60 - 70.95)²/70.95 = 1.69
Under 3 37 215 * 0.08 = 17.2 (37 - 17.2)²/17.2 = 22.793
Total 215 215 27.4846

The correct hypotheses are:

H0: The regional distribution is a good fit to the national distribution.

HA: The regional distribution is not a good fit to the national distribution.(claim)

Test statistic:  

χ² = ∑ ((O-E)²/E) = 27.485

df = n-1 = 3

p-value = CHISQ.DIST.RT(27.4846, 3) = 0.000

----------------------------

Question 2:

Action Observed Frequency (O) Expected Frequency (E) (O-E)²/E
On time 180 250 * 0.71 = 177.5 (180 - 177.5)²/177.5 = 0.0352
National Aviation System Delay 18 250 * 0.08 = 20 (18 - 20)²/20 = 0.2
Aircraft Arriving late 20 250 * 0.08 = 20 (20 - 20)²/20 = 0
Other 32 250 * 0.13 = 32.5 (32 - 32.5)²/32.5 = 0.0077
Total 250 250 0.2429

The correct hypotheses are:

H0: The sample is a good fit to the Bureau of Transportation Statistics.

HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim)

Test statistic:  

χ² = ∑ ((O-E)²/E) = 0.243

df = n-1 = 3

p-value = CHISQ.DIST.RT(0.2429, 3) = 0.970

----------------------------

Question 3:

AGE Observed Frequency (O) Expected Frequency (E) (O-E)²/E
5 Years 20 202 * 0.1 = 20.2 (20 - 20.2)²/20.2 = 0.002
4 Years 99 202 * 0.5 = 101 (99 - 101)²/101 = 0.0396
3 Years 46 202 * 0.28 = 56.56 (46 - 56.56)²/56.56 = 1.9716
Under 3 37 202 * 0.12 = 24.24 (37 - 24.24)²/24.24 = 6.7169
Total 202 202 8.7301

The correct hypotheses are:

H0: The regional distribution is a good fit to the national distribution.

HA: The regional distribution is not a good fit to the national distribution.(claim)

Test statistic:  

χ² = ∑ ((O-E)²/E) = 8.730

df = n-1 = 3

p-value = CHISQ.DIST.RT(8.7301, 3) = 0.033

----------------------------

Question 4:

Action Observed Frequency (O) Expected Frequency (E) (O-E)²/E
On time 159 230 * 0.68 = 156.4 (159 - 156.4)²/156.4 = 0.0432
National Aviation System Delay 21 230 * 0.07 = 16.1 (21 - 16.1)²/16.1 = 1.4913
Aircraft Arriving late 21 230 * 0.08 = 18.4 (21 - 18.4)²/18.4 = 0.3674
Other 29 230 * 0.17 = 39.1 (29 - 39.1)²/39.1 = 2.609
Total 230 230 4.5109

The correct hypotheses are:

H0: The sample is a good fit to the Bureau of Transportation Statistics.

HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim)

Test statistic:  

χ² = ∑ ((O-E)²/E) = 4.511

df = n-1 = 3

p-value = CHISQ.DIST.RT(4.5109, 3) = 0.211

milcah answered 7 months ago
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