Solve by hand. Do not use any external softwares or programs including Excel. orA random sample of reviews were taken from Spotify for both singers, 300reviews for Harry Styles and 200 reviews for Taylor Swift.SingerAverage Rating (stars)Standard Deviation of the RatingsHarry Styles3.51Taylor Swift4.051.030.98(a) What probability distribution would you use to test the hypothesis that both signershave the same average rating? Explain.(b) Test the hypothesis that both singers have the same average rating, using a 5%significance level. What are your conclusions? What is the p value for this test?(f) Construct a 95% confidence interval for Taylor Swift having a higher rating than HarryStyles. What does this tell us about which singer is more popular?

Given,the average rating for two star singers along with their standard deviations.To formulate the test used for the difference between the average ratings of the two stars, test the hypothesis, and construct a 95% confidence interval.(a). Sample sizes are greater than 30. So, the Z-test for the difference between two means is used to test the average ratings for both singers.(b). Null hypothesis - Alternative hypothesis - .Level of significance - .Test statistic - p-value - Since the p-value is less than the level of significance, the null hypothesis is rejected at a 0.05 level of significance..Both singers have no same average rating.(f).The 95% confidence interval for Taylor Swift has a higher rating than Harry stylesStyles is - Since the confidence interval is in the positive range, i.e. greater than zero, Taylor Swift is more popular than Harry styles.(a). The Z-test for the difference of two means is used to test the average ratings for both singers.(b). Both singers have no same average rating.(c). The 95% confidence interval for Taylor Swift has a higher rating than Harry styles is. .Since the confidence interval is in the positive range, i.e. greater than zero, Taylor Swift is more popular than Harry styles.