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2 answers:
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Answer:
1a) p-hat=0.38
1b) P=0.08
1c) The null hypothesis is not rejected
2a) p-hat=0.64
2b) P=0.0027
2c) The null hypothesis is rejected
3a) p-hat=0.55
3b) P=0.153
3c) The null hypothesis is not rejected
Step-by-step explanation:
(1) H0: p = 0.3 vs Ha: p ≠ 0.3. In their survey, they had a count of 38 using a sample size n=100.
1a) The p-hat is p-hat=38/100=0.38.
1b) The standard deviation is
The sample size is n=100.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=1.74 is P=0.08.
1c) The null hypothesis is not rejected.
(2) H0: p = 0.7 vs Ha: p ≠ 0.7. In their survey, they had a count of 320 using a sample size n=500.
2a) The p-hat is p-hat=320/500=0.64.
2b) The standard deviation is
The sample size is n=500.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=3 is P=0.0027.
2c) The null hypothesis is rejected.
(3) H0: p = 0.6 vs Ha: p < 0.6. In their survey, they had a count of 110 using a sample size n=200.
2a) The p-hat is p-hat=110/200=0.55.
2b) The standard deviation is
The sample size is n=200.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=1.43 is P=0.153.
2c) The null hypothesis is not rejected.
Answer/Step-by-step explanation:
Score 1:
3, 7, 5, 4, 5, 6, 7, 8, 6, 5
Mean =
Median: order the data from least to the greatest.
3, 4, 5, 5, 5, 6, 6, 7, 7, 8
The median is average of the fifth and sixth data value in the data set
Median = (5 + 6)/2 = 11/2 = 5.5
Mode = value with the highest frequency = 5
Score 2:
34, 54, 17, 26, 34, 25, 14, 24, 25, 23
Mean = sum of all values/10
Mean = 276/10 = 27.6
Median: order the data set from min to max.
14, 17, 23, 24, 25, 25, 26, 34, 34, 54
The median is average of the fifth and sixth data value in the data set
Median = (25 + 25)/2 = 50/2 = 25
Mode = 25 and 34 (both have frequencies of 2)
Score 3:
154, 167, 132, 145, 154, 145, 113, 156, 154, 123
Mean = sum of all values/10
Mean = 1443/10 = 144.3
Median: order the data set from min to max.
113, 123, 132, 145, 145, 154, 154, 154, 156, 167
The median is average of the fifth and sixth data value in the data set
Median = (145 + 154)/2 = 299/2 = 149.5
Mode = 154