Q4) The following yields were recorded by usingtwo agricultural products.

Perform a two sample hypothesis test to consider if the yieldsfor product A and product B are different. Use the defaultsignificance level of α=0.05.

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

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

YieldA                         Â	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.

1. Calculate thetest-statistic.    (state accurate to2dp)

1. State the Degrees of Freedom.

(1 Mark)

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

(1 Mark)

1. State your decision regarding H_o.

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

Perform a hypothesis test to determine if there is anassociation between patients being given anti-viral drugs anddeveloping 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 conditionof the Null hypothesis.

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

1. Calculate the two missing χ² contributions to thetest-statistic.

                                                                                       (stateaccurate to 4dp)

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

1. Calculate the test statistic,χ²Â Â (state accurateto 2dp).

(1 mark)

1. Look up the critical value from tables and state itsvalue.

(1 mark)

1. State your decision to reject or not reject H_o andconfirm or deny whether there is a relationship between drugtreatment and pneumonia.

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

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 meanprice of the product in the city. State the intervalaccurate to 1 decimalplace.                                                                                                

1. Is it reasonable to assume that the average price for thisproduct is £100? State yourreasoning.                                                                                                                      

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