13.Government officials in Manitoba would like to determine if the average entry level annual income of women working in the tech industry has increased since 2014. Researchers at the University of Manitoba determined that in 2014 the average entry level annual income for women working in a technology related profession (e.g., Artificial Intelligence) was $91,000 with a standard deviation of $1,400. The research team conducted a survey in 2021 where they randomly sampled 51 female working professionals who have been employed in a technology related field for less than 14 months. They determined that the sampled women had a mean annual income of $90,000 with a standard deviation of $2,000. Annual income is known to follow a normal distribution.

Conduct a hypothesis test at the 8% level of significance to determine if there is evidence that the true mean annual income in 2021 increased compared to 2014. Provide the following:

(d)test statistic value, please indicate type of test being used (z or t)

(e)P-value

(f)conclusion

14.The province of Manitoba is interested to estimate the true proportion of people who have received the first COVID-19vaccine.A study was conducted to address this concern. A random sample of 100 people were selected (who were eligible for the vaccine), 45 of whom said they have received the vaccine.

(a) Construct a 95% confidence interval for estimating the true population proportion

(b) Provide an interpretation of the confidence interval in part (a). (1 mark)

Conduct an appropriate hypothesis test, at the 10% level of significance to test the claim that less than 48% of Winnipeggers received the vaccine. Provide the following:

(d)test statistic value, please indicate type of test being used

(e)P-value

(f)conclusion

15.A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is greater than 0.90, a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

Select one:

a. 2.33

b. -2.33

c. -1.67

d. 0.14

e. - 1.86

16.studying per week is 1.9 hours. She randomly asks 12 students to keep track of and report the time they spend studying per week.The average time spent by these 12 students is:

0.25,

1,

2,

2.2,

2.5,

0.75,

2.5,

3,

2,

3.3,

3.9,

2.9.

Conduct an appropriate hypothesis test, at the 1% level of significance to determine if the amount of time spent by the 12 students exceeds 1.9 hours. Provide the following:

(b)test statistic value, please indicate type of test being used (z or t)

(c)P-value

(d)conclusion