I NEED ALL ANSWERS ASAP
(a) give brief explanations for each of the following terms:
(i) random sample
(ii) quota sample
(b) in a sample of 30 chocolate bars, it is found that the mean weight is 100gms.
with a standard deviation of 1.9gms. Construct of 95% confidence interval for the true
mean weight of the chocolate bars
(a)
(i) Random sample: A random sample is a subset of a population that is chosen in such a way that every member of the population has an equal chance of being included in the sample. This sampling method helps to ensure that the sample is representative of the entire population and reduces the potential for bias.
To obtain a random sample, you can use various methods, including simple random sampling where each member of the population is assigned a number and then a random number generator is used to select the sample, or stratified random sampling where the population is divided into subgroups and a random sample is taken from each subgroup.
(ii) Quota sample: A quota sample is a non-random sampling technique where the researcher selects a sample that matches certain predetermined quotas or characteristics. These quotas are usually based on specific demographics, such as age, gender, or income level.
In a quota sample, the researcher establishes proportions for each characteristic or quota in the sample that reflect the proportions in the overall population. This sampling method is often used when it is difficult to obtain a truly random sample or when the researcher wants to ensure representation of specific groups in the sample. However, quota sampling can introduce bias if the chosen quotas do not accurately reflect the population.
(b) To construct a 95% confidence interval for the true mean weight of the chocolate bars, you can use the following formula:
Confidence Interval = mean ± (critical value * standard deviation / square root of sample size)
In this case, the mean weight is 100gms and the standard deviation is 1.9gms. From the given information, we don't have the sample size mentioned, but let's assume it is n = 30.
Next, you need to determine the critical value for a 95% confidence interval. For a normal distribution, the critical value corresponds to the two-tailed z-value at a confidence level of 95%, which is approximately 1.96.
Finally, you can substitute the values into the formula to calculate the confidence interval:
Confidence Interval = 100 ± (1.96 * 1.9 / √30)
Now, you can compute the confidence interval using the given values and the formula.