Question

Q4) The following yields were recorded by using two agricultural products.

Perform a two sample hypothesis test to consider if the yields for product A and product B are different. Use the default significance level of α=0.05.

You may assume that the population variances for product A and B are equal.

You should take the mean of Yield A first in your test statistic.

Yield A	Yield B
452	546
874	547
554	774
447	465
356	459
754	665
558	467
574	365
664	589
682	534
547	456
435	651
245	665
	546
	537
	654

1. State the Null and Alternative hypotheses.

2. Calculate the test-statistic.    (state accurate to 2dp)

3. State the Degrees of Freedom.

(1 Mark)

4. Look up the upper-tail critical value from tables.

(1 Mark)

5. State your decision regarding H_o.

Q5) 184 patients with coronavirus have been hospitalised in the city hospital. 92 have been treated with anti-viral medication and 92 have not.  

Perform a hypothesis test to determine if there is an association between patients being given anti-viral drugs and developing pneumonia. Use a 5% level of significance.

The Observed frequencies are presented in the table below.

	Treated with anti-viral drugs
	With drugs	No drugs given	Total
Pneumonia	31	15	46
No pneumonia	61	77	138
Total	92	92	184

1. Calculate the four expected values under the condition of the Null hypothesis.

	Expected Values
	With drugs	No drugs given	Total
Pneumonia			46
No pneumonia			138
Total	92	92	184

2. Calculate the two missing χ² contributions to the test-statistic.

                                                                                       (state accurate to 4dp)

	Contributions to the χ2 test statistic
	With drugs	No drugs given
Pneumonia	2.7826
No pneumonia		0.9275

3. Calculate the test statistic, χ²  (state accurate to 2dp).

(1 mark)

4. Look up the critical value from tables and state its value.

(1 mark)

5. State your decision to reject or not reject H_o and confirm or deny whether there is a relationship between drug treatment and pneumonia.

Q6) A sample of the various prices for a particular product has been conducted in 16 stores which were selected at random in a city. The following prices were noted, in GBP:

95, 108, 97, 112, 99, 106, 105, 100, 99, 98, 104, 110, 107, 111, 103, 110.

1. Calculate a 95% confidence interval to estimate the actual mean price of the product in the city. State the interval accurate to 1 decimal place.                                                                                                

2. Is it reasonable to assume that the average price for this product is £100? State your reasoning.                                                                                                                      

3. What size sample would need to be taken to estimate the population mean price within 1 pound?                                                                                                                    

Answer 1