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
(c) in a survey of 1100 work places. it is found that 935 conform to safety regulations
construct an approximate 95% confidence for the true proportion of work places conforming
to safety regulations
(d) one section of a pharmaceutical manufacturing plant is designed to have a mean
temperature of -10°C. The temperature is measured 19 times over the course of a day and
it is found that the sample mean is -9.7°C, while there is a sample standard deviation
of 0.35°C. Does the evidence indicate (at the 5% significance level) that the mean
temperature is different to -10°C?
As I told @Mairead ,we cannot do your work for you. Next time please ask one question, instead of posting a full test.
Do part of it at least
(a) Here are brief explanations for each of the following terms:
(i) Random sample: A random sample is a subset of individuals or items from a larger population that is selected in such a way that every member of the population has an equal chance of being included in the sample. Random sampling helps to ensure that the sample is representative of the population.
(ii) Quota sample: A quota sample is a non-random sampling method where certain characteristics or quotas are set in advance, and participants are selected to meet those quotas. This method is often used when researchers want to ensure that the sample represents specific subgroups within the population.
To obtain answers to questions (b), (c), and (d), we need to perform some calculations and statistical tests. Here's how you can approach each of these questions:
(b) To construct a confidence interval for the true mean weight of the chocolate bars:
1. Determine the sample mean weight (given as 100gms) and sample standard deviation (given as 1.9gms).
2. Determine the sample size (given as 30).
3. Use the formula for a confidence interval for the mean: mean ± (critical value * standard deviation / √sample size).
4. Look up the critical value for a 95% confidence level in the t-distribution table using the appropriate degrees of freedom (n-1) for the sample size.
5. Plug in the values into the formula to calculate the lower and upper limits of the confidence interval.
(c) To construct an approximate confidence interval for the true proportion of workplaces conforming to safety regulations:
1. Determine the sample size (given as 1100) and the number of workplaces conforming to safety regulations (given as 935).
2. Calculate the sample proportion (935/1100).
3. Use the formula for a confidence interval for a proportion: proportion ± (critical value * √(proportion*(1-proportion)/sample size)).
4. Look up the critical value for a 95% confidence level in the standard normal distribution table.
5. Plug in the values into the formula to calculate the lower and upper limits of the confidence interval.
(d) To test whether the evidence indicates that the mean temperature is different from -10°C:
1. Determine the sample mean temperature (given as -9.7°C), the sample standard deviation (given as 0.35°C), and the sample size (given as 19).
2. Define the null hypothesis (H0) stating that the mean temperature is equal to -10°C, and the alternative hypothesis (Ha) stating that the mean temperature is different from -10°C.
3. Perform a t-test using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size).
4. Look up the critical value for a 5% significance level in the t-distribution table using the appropriate degrees of freedom (n-1) for the sample size.
5. Compare the calculated test statistic (t) with the critical value. If the calculated test statistic falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
It is important to note that access to specific data and statistical software may be required to perform the calculations accurately.