Hypothesis Testing (variances & proportions)
1. Freezer:
A commercial freezer must hold the selected temperature with little variation. Specifications call for a standard deviation of no more than 3 degrees. A sample of 16 freezers is tested and yields a sample standard deviation of s = 3.8. Test to see whether the variation specification is exceeded at the 0.05 level of significance.
2. Waiting time:
For years a large discount store has used independent lines to check out customers. Historically the standard deviation of waiting times is 7 minutes. The manager tried a new single-line procedure. A random sample of 25 customers using single-line procedure was monitored and it was found that the standard deviation for waiting times was s = 5.25 minutes. Use a 0.10 level of significance to test the claim that single-line procedure reduces the variability in waiting times.
3. Marriage age:
The age of Pakistani rural women at their first marriage is normally distributed with a standard deviation of 4.3 years. A random sample of 50 married rural women from the north-western province reveals a standard deviation of 3.6 years. Is there enough evidence at the 0.05 level of significance to claim that marriage age variability in the north-western province is less than the rest of the country?
4. Diet:
A particular weight-loss diet achieves, after 6 months, satisfactory results on average, but its variability is relatively high (σ=2.8 kg). A new modification to the diet has been implemented and a random sample of 25 people using this modified diet for 6 months was surveyed. The sample reveals a standard deviation of s=1.9 kg. Can we claim, at the 0.01 level of significance, that the new modification reduces the weight-loss variability of the diet?
5. Home ownership
A recent survey found that 68.6% of the population in the country own their homes. In a random sample of 150 heads of households, 92 responded that they owned their homes. At the α = 0.01 level of significance, does that suggest a difference from the national proportion?
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Hypothesis Testing (variances & proportions)
1. Freezer:
A commercial freezer must hold the selected temperature with little variation. Specifications call for a standard deviation of no more than 3 degrees. A sample of 16 freezers is tested and yields a sample standard deviation of s = 3.8. Test to see whether the variation specification is exceeded at the 0.05 level of significance.
2. Waiting time
For years a large discount store has used independent lines to check out customers. Historically the standard deviation of waiting times is 7 minutes. The manager tried a new single-line procedure. A random sample of 25 customers using single-line procedure was monitored and it was found that the standard deviation for waiting times was s = 5.25 minutes. Use a 0.10 level of significance to test the claim that single-line procedure reduces the variability in waiting times.
3. Marriage age:
The age of Pakistani rural women at their first marriage is normally distributed with a standard deviation of 4.3 years. A random sample of 50 married rural women from the north-western province reveals a standard deviation of 3.6 years. Is there enough evidence at the 0.05 level of significance to claim that marriage age variability in the north-western province is less than the rest of the country?
4. Diet:
A particular weight-loss diet achieves, after 6 months, satisfactory results on average, but its variability is relatively high (σ=2.8 kg). A new modification to the diet has been implemented and a random sample of 25 people using this modified diet for 6 months was surveyed. The sample reveals a standard deviation of s=1.9 kg. Can we claim, at the 0.01 level of significance, that the new modification reduces the weight-loss variability of the diet?
5. Home ownership
A recent survey found that 68.6% of the population in the country own their homes. In a random sample of 150 heads of households, 92 responded that they owned their homes. At the α = 0.01 level of significance, does that suggest a difference from the national proportion?